**Scanning Electron Microscopy Analysis and Energy Dispersion X-ray Microanalysis to Evaluate the E**ff**ects of Decontamination Chemicals and Heat Sterilization on Implant Surgical Drills: Zirconia vs. Steel**

**Antonio Scarano 1,2,3,\*, Sammy Noumbissi 2,4, Saurabh Gupta 2,5, Francesco Inchingolo 6, Pierbiagio Stilla <sup>1</sup> and Felice Lorusso <sup>7</sup>**


Received: 3 June 2019; Accepted: 10 July 2019; Published: 16 July 2019

#### **Featured Application: The control of the e**ff**ect of drills wear and corrosion related to clinical use represents a critical factor in implantology, because it is strictly related to the bone cutting precision and heat generation during site preparation.**

**Abstract: Background:** Drills are an indispensable tool for dental implant surgery. Today, there are ceramic zirconium dioxide and metal alloy drills available. Osteotomy drills are critical instruments since they come in contact with blood and saliva. Furthermore, they are reusable and should be cleaned and sterilized between uses. Depending on the material, sterilizing agents and protocols can alter the surface and sharpness of implant drills. The hypothesis is that cleaning and sterilization procedures can affect the surface structure of the drills and consequently reduce their cutting efficiency. **Methods:** Eighteen zirconia ceramic drills and eighteen metal alloy drills were evaluated. Within the scope of this study, the drills were not used to prepare implant sites. They were immersed for 10 min in human blood taken from volunteer subjects and then separately exposed to 50 cycles of cleansing with 6% hydrogen peroxide, cold sterilization with glutaraldehyde 2%, and autoclave heat sterilization. Scanning Electron Microscopy (SEM) and energy dispersion X-ray (EDX) microanalysis were conducted before and after each cycle and was used to evaluate the drill surfaces for alterations. **Results:** After exposure to the cleansing agents used in this study, alterations were seen in the steel drills compared to zirconia. **Conclusions:** The chemical sterilization products used in this study cause corrosion of the metal drills and reduce their sharpness. It was observed that the cycles of steam sterilization did not affect any of the drills. Zirconia drill surfaces remained stable.

**Keywords:** implant drills; zirconium dioxide; sterilization; disinfection; cleaning; corrosion; implant failure

#### **1. Introduction**

Drill wear is a phenomenon determined by the detachment of particles during the preparation of implant sites that can interfere with the process of bone healing. Considering that all materials are subject to wear and chemical attack by disinfectants, it would be desirable to have a biocompatible drill that is not susceptible to attack by the disinfectants used in clinical practice. The healing of peri-implant bone is a complex phenomenon that involves the proliferation and differentiation of pre-osteoblasts into osteoblasts. Periosteal and endosteal activity also contributes to the production of the osteoid matrix, which is followed by mineralization and organization of the bone–implant interface [1]. The success of implant surgery depends on the bone and soft tissue healing after the process of implant site preparation [2]. One of the key factors in implant success is to keep the osteotomy process as atraumatic as possible for fast, optimal recovery and healing. One of the most important factors in minimizing trauma during osteotomy is to control heat generation with irrigation, but also by utilizing drills that will cut through bone in an efficient and minimally invasive manner [3,4]. Even after a single use, drills will show signs of wear and start to lose their sharpness and cutting efficiency [5,6]. A slightly damaged or dulled drill will not only lose its cutting efficiency, but also overheat bone, leading to bone necrosis, poor healing, and an ill-defined osteotomy with a poor initial implant stability [7,8]. Among the materials used for the manufacturing of implant drills is steel, whose structural integrity can be affected by disinfectants and cleaning agents. When coming into contact with chemical disinfectants, an oxidation process takes place on the drill, giving rise to corrosion products and the release of metal particles and ions to the peri-implant tissues, which can cause inflammation, increased osteoclastic activity, and subsequent implant failure [9,10].

The phenomenon and mechanism by which the reuse of an implant drill can be a source of metal particles or ions in implant bed preparation have not been evaluated in the literature. Metal particles and ions are known to induce osteolysis, so it is important to avoid potential sources of metal ions and particles for the long-term survival of dental implants. The reuse of drills, repeated cleansing, and sterilization causes them to lose their sharpness and trigger the corrosion process. As a result, there is a loss of cutting efficiency, thus making it possible to leave metal particles and ions in the bone. Furthermore, the loss of cutting efficiency increases the friction between the bone and drills and elevates the osteotomy temperature, leading to bone cell death and implant failure. An alternative drill material to steel is zirconium dioxide, also known as zirconia, which is a ceramic and belongs to the category of materials called inert metal oxides. They are also used as dental implant materials [11]. Zirconia is bio-inert, and has excellent corrosion resistance, superior biocompatibility, high wear resistance, and high fracture resistance values [12,13]. Repeated disinfection and sterilization cycles can lead to undesirable changes in the physical properties of the instruments, such as a loss of structure, sharpness, and corrosion [5]. The purpose of this study is to analyze the effects of chemical disinfection and autoclave sterilization on zirconium oxide ceramic drills vs. steel drills by scanning electron microscopy and energy dispersion X-ray microanalysis. The null hypothesis of this study is that there will be no difference in surface alterations between zirconia and steel drills as a result of disinfection and sterilization procedures.

#### **2. Materials and Methods**

In this study, a total of 18 drills of zirconia (Dental Tech, Misinto, Milan) and 18 steel drills were used (Dental Tech, Misinto, Milan) (Figure 1).

**Figure 1.** Macroscopic aspect of the steel drill (left) and zirconia drill (right) used in the present study.

Only 2 mm diameter helical conical drills were evaluated in order to analyze their response to disinfecting and cleansing agents, as well as autoclave sterilization. The steel drills presented the following chemical composition: 0.2% sulfur, 0.2% carbon, 0.6% silicon, 0.8% nickel, 1.2% molybdenum, 1.6% manganese, 16% chromium, 22% carbon, and balancing iron. The chemical composition shows the typical characteristics of a stainless-steel alloy. The drills studied were all externally irrigated and had three black laser markings with the function of guiding the surgeon in controlling the depth during osteotomy. In this investigation, chemical agents such as glutaraldehyde 2% (Dimexid, Amedics Ferrara, Italy) and hydrogen peroxide 6% (Sanibios, Noda, Balerna- Switzerland), were taken into consideration, and the effect of sterilization cycles was also observed. The drills were not subjected to the preparation of implant sites, but were immersed for 10 minutes in human blood taken from voluntary subjects and then underwent cycles of immersion in disinfectants without being subjected to autoclaving (approved by Inter Institutional Ethics Committee of UNINGÁ, No. 72105917.5.0000.5220). Before immersion, decontamination, or sterilization, the drills were rinsed in running water and scrubbed with a toothbrush made of nylon bristles in order to remove gross foreign material (e.g., organic material, clot). A total of 18 steel drills and 18 zirconia drills were used and allotted to 6 groups of 6 drills, with 6 in steel and 6 in zirconia for each group. Then, implant drills were assessed before and after the disinfection by Scanning Electron Microscopy (SEM). A disc of carborundum was used to separate the blades from the grips of the drills to be observed by SEM. Ten flat areas of 200 μm to 150 μm in diameter were evaluated for each drill and an image in JPEG format was created (Figure 2).

**Figure 2.** The flat area evaluated for each drill.

The drills were divided into the following groups:

Group 1: New non-sterilized Steel drill; Steel drills subjected to 50 cycles of 20 min sterilization immersion in glutaraldehyde;

Group 2: Steel drills subjected to 50 immersion cycles of 20 min immersion cleansing in hydrogen peroxide;

Group 3: Steel drills subjected to 50 cycles of heat sterilization in an autoclave at 134◦ C for 35 min at a pressure of 1.1 bar; New non-sterilized Zirconia drills;

Group 4: Zirconia drills subjected to 50 cycles of 20 min immersion sterilization in glutaraldehyde; Group 5: Zirconia drills subjected to 50 immersion cycles of 20 min for cleansing in

hydrogen peroxide;

Group 6: Zirconia drills subjected to 50 cycles of heat sterilization in an autoclave at 134◦ C for 35 min at a pressure of 1.1 bar (A-17 PLUS, ANTHOS, Imola, Italy).

All the solutions were poured into a plastic container in order to avoid interference between the liquid and metal. In accordance with the Italian legislation DMS of 28/9/90, the drills were immersed for 20 min in a liquid chemical sterilant. After 50 cycles of decontamination and cold sterilization immersion, the drills were rinsed in running water and then in demineralized water. They were then observed by a transmission electron microscope. The method of analysis followed the methodology proposed by Scarano et al. [5].

Previously calibrated examiners compared the micrographs before and after 50 cycles of disinfection and sterilization, respectively, with those obtained for the control group and assessed the percentage of surface covered by damage.

#### *2.1. SEM Observations*

In order to evaluate changes in the surface topography, we used a scanning electron microscope (SEM, JSM-6480LV; Jeol, Tokyo, Japan), with a solid-state backscattered detector operated at a 20 kV accelerating voltage. Each drill was attached to an aluminum stub with sticky conductive carbon tape. Images were taken in both secondary and backscattered electrons. The drills were mounted on aluminum stubs and gold-coated in Emitech K550 (Emitech Ltd., Ashford, UK). Pictures were recorded for each specimen to characterize the surface and presence of corrosion area. The pictures were processed with ImageJ (ImageJ, U.S. National Institute of Health, Bethesda, MD, USA).

#### *2.2. Energy Dispersive X-ray Spectroscopy (EDX)*

To detect possible drill alterations, the drills were examined before and after sterilization with a scanning electron microscope/energy dispersion X-ray microanalysis (SEM/EDX) using scanning electron microscopy (SEM, JSM-6480LV; Jeol, Tokyo, Japan) with the EDS QUANTAX-200 probe (Bruker Nano GmbH, Berlin, Germany).

#### *2.3. Statistical Evaluation*

Free software available on the site http://clincalc.com/stats/samplesize.aspx, was used to determine the number of drills needed to achieve statistical significance for quantitative analyses of drill surface damage. A calculation model was adopted for dichotomous variables (yes/no effect) by applying the effect incidence designed to caution the reasons, with values of 10% for zirconia drill and 95% for steel drill, and the alpha was set at 0.05 and power at 70%. The optimal number of specimens for analysis was six drills per group.

A normal data distribution was evaluated by the Shapiro–Wilk test and the differences between the groups were analyzed by one-way analysis of variance (ANOVA) followed by a Tukey post-hoc test. A *p*-value < 0.05 was considered statistically significant. Data processing and statistical analysis were performed by Excel origin and SPSS software (SPS, Bologna, Italy).

#### **3. Results**

*Scanning Electron Microscopy Analysis and Energy Dispersion X-ray Microanalysis*.

#### *3.1. Steel Drills*

#### *New Non-Sterilized Drill*

The spectroscopic analysis showed that the flat area of implant drills was composed of stainless-steel alloys with a high content of iron, nickel, and chromium (Figure 3).

#### Group 1

After 50 cycles of decontamination, the drills immersed in the glutaraldehyde showed traces of corrosion with deposits on the bottom of the container and traces of a rust color. The drills appeared to be macroscopically damaged and the laser depth markings were less distinctive, but still identifiable. The areas of corrosion were mostly present especially near the laser markings (Table 1). In total, 21 ± 3% of the drill surface in this group was covered by damage (Figure 4). None of the drills had surface damage over 30% of the total surface. The spectroscopic analysis of the drill surface showed a reduction in iron, nickel, and chromium and a comparable increase in oxygen (Figure 5).

#### Group 2

The drills immersed in hydrogen peroxide appeared to be macroscopically damaged, but the damaged surface areas were smaller and the laser depth marks remained clearly visible. A total of 12 ± 1% of the drill surface in the hydrogen peroxide group was covered by damage. No drill in this group had damage above 20% of the surface (Figure 6). Additionally, in this group, the spectroscopic analysis of the drill surface showed a decrease in iron levels and a comparable increase in oxygen.

#### Group 3

The steel drills that were subjected to 50 cycles of heat sterilization by steam neither caused areas of corrosion nor altered the depth notches (Table 1) (Figure 7). The spectroscopic analysis of the drill surface showed a smaller increase in oxygen and a decrease in the levels of iron, nickel, and chromium (Figure 8).

**Figure 3.** Spectra showing elemental peaks of the new drill surface.

**Figure 4.** Group 1. Aspects of the steel drill after 50 disinfection cycles with glutaraldehyde, where zones of structural alteration can be observed.

**Figure 5.** Group 1. The spectroscopic analysis of the drill surface after 50 disinfection cycles with glutaraldehyde showed a decrease in oxygen, iron, nickel, and chromium.

**Figure 6.** Group 2. After 50 disinfection cycles with hydrogen peroxide, zones of damage by the corrosive process were observed (arrows).

**Figure 7.** Group 3. After 50 steam autoclave cycles, no areas of corrosion were observed.

**Figure 8.** Group 3. The spectroscopic analysis of the drill surface after 50 steam autoclave cycles, where no changes in iron, nickel, and chromium levels and a smaller increase in oxygen where observed.

#### *3.2. Zirconia Drills*

#### *New Non-Sterilized Drill*

The spectroscopic analysis of the new unsterilized zirconia drill surface showed that the flat areas of implant drills were mainly composed of zirconia and carbon, oxygen, and aluminum (Figure 9).

#### Group 4

The zirconia ceramic drills observed after 50 cycles of immersion in the glutaraldehyde had the same appearance as the new non-sterilized drills and did not have residues of organic material (Figure 10). The spectroscopic analysis of the drill surface showed no change in the surface composition.

#### Group 5

The zirconia ceramic drills observed after 50 cycles of immersion in the hydrogen peroxide had the same appearance as the new non-sterilized drills and did not have residues of organic material (Figure 11). The spectroscopic analysis of the drill surface showed no change in the surface composition.

#### Group 6

No damage was detected after 50 cycles of heat sterilization in the autoclave, and there was no corrosion or alteration of the laser markings (Figure 12). No differences were observed between the different disinfection liquid immersions (glutaraldehyde and hydrogen peroxide). The black notches that showed the depth and the numbers printed on the drill shanks were intact and showed no signs of damage.

The spectroscopic analysis of the drill surface showed no change in the surface composition.

**Figure 9.** The spectroscopic analysis of the new zirconia drill surface showed that the flat area of implant drills was mainly composed of zirconia.

**Figure 10.** Group 4. The zirconia drill viewed under a scanning electron microscope after 50 disinfection cycles with glutaraldehyde. Sharp margins are free from defects.

**Figure 11.** Group 5. The zirconia drill after 50 disinfection cycles with hydrogen peroxide, where no damage was observed on the cutting edges or deposits of other substances.

**Figure 12.** Group 6. After 50 steam autoclave cycles, no areas of corrosion were observed.

**Table 1.** Summary of the drills surface area damaged by the testing processes. The disinfection processes generated significant surface corrosion compared to the zirconia drills (*p* < 0.01). The autoclave sterilization did not cause any alteration to the different drill surfaces.


\*\* *p* < 0.01.

#### *3.3. Statistical Analysis*

The SEM results showed the drill surface covered by damage and corrosion percentages for the steel drill. A statistically significant difference was found in the percentage of drill surface covered by damage and corrosion on the zirconia drill compared to the steel implant drills (*p* = 0.000034) (Figure 13).

**Figure 13.** Differences in surface alteration occurred in the different study groups.

#### **4. Discussion**

In clinical practice, it is important to avoid cross-infection and it is for this reason that the drills should be treated with disinfectant chemicals, thoroughly rinsed, and submitted to autoclave heat sterilization.

In this study, we used two different disinfection chemicals, namely glutaraldehyde and hydrogen peroxide, which both provide high-level disinfection. The outcomes of the present research showed that zirconia drills are more resistant to the corrosive action of disinfecting chemicals. In fact, a greater difference was found in the percentages of drill covered by surface damage. SEM analysis demonstrated that repeated autoclave sterilization cycles had no effect on the zirconia and steel drills.

The purpose of the present investigation was to study the influence of disinfection and sterilization on the implant drill surfaces. The authors hypothesized that zirconia drills may offer a greater resistance to the action of disinfectants commonly used in clinical practice.

The contact with contaminated surfaces produces destructive hydroxyl free radicals that can attack DNA, membrane lipids, and other essential cell components. Glutaraldehyde is a saturated dialdehyde that has gained wide acceptance as a high-level disinfectant and chemical sterilant [14]. Aqueous solutions of glutaraldehyde are "activated" by using alkalinating agents to bring the pH to values between 7.5 and 8.5, which makes the solution sporicidal [15,16]. Glutaraldehyde (GAA) solutions are used for the sterilization of medical devices, such as endoscopes and fibroscopes. Hydrogen peroxide has good bactericidal, sporicidal, viricidal, and fungicidal properties [17]. However, both glutaraldehyde and hydrogen peroxide are corrosive to steel instruments.

Implant drills are reusable medical devices and implant bed preparation with drills is an invasive procedure involving contact of the drill with blood, bone, and other biological fluids. The major risk of all such procedures is the introduction of drill particles and transfer of pathogens, potentially leading to infection [18]. The main objective of disinfecting or sterilizing drills is to eliminate the transmission of pathogens by means of contaminated medical and surgical devices (e.g., HIV, HCV, *Mycobacterium tuberculosis*, and encephalopathies) [19,20]. Today, the disinfection of medical devices such as implant drills is very important for preventing the emergence of transmissible spongiform, such as the encephalopathies (TSEs), which is a prion protein less susceptible to denaturation by heat and is responsible for disease such as variant Creutzfeldt–Jakob [21]. Therefore, the predicable cleaning of implant drills is believed to be a key procedure for reducing the risks of onward transmission of infectious diseases and pathogens such as human immunodeficiency virus (HIV), hepatitis B and C, gram-negative and gram-positive bacteria, fungi, and preventing the risk of mycobacteria transmission. In addition to microbial inactivation, the removal of organic or inorganic debris is crucial as it may compromise subsequent disinfection or sterilization processes [22]. The cleaning of reusable implant drills is also important in order to ensure drill longevity and efficiency in cutting bone, also making the removal of organic and chemical residues important. The effect of liquid chemical sterilant depends on cleaning to eliminate organic and inorganic material, an optimal pH, concentration, contact time, and temperature are all paramount. During chemical disinfection, it is important that implant drills are not mixed with other drills, or other instruments of different material composition in order to avoid chemical corrosion. In this study, once chemical disinfection was completed, we proceeded to heat sterilization at 134 ◦C (273 ◦F) for 35 min.

It is known that the effect of disinfectants and sterilization can influence the cutting efficiency of drills [5,23]. The material that constitutes an osteotomy drill must also have a good resistance to corrosion, which is one of the factors responsible for the loss of cutting efficiency. The drills used for the preparation of implant sites must undergo decontamination and sterilization procedures before being reused on another patient. After every use, reusable medical devices must be rinsed, cleaned, and immediately immersed in an approved medical grade chemical disinfectant with a recognized effectiveness against HIV in accordance with Italian legislation art. 2 Ministerial Decree 28.09.90 [24]. The Ministerial Decree (DMS) imposes a set of rules for the protection of professionals from a broad range of infections in public and private health and care facilities. The objectives of these precautions

are to prevent the transmission of pathogenic organisms through blood and biological fluids. The cleansing occurs as a result of the chemical actions of a detergent that must be used at recommended concentrations and contact times. It is necessary to frequently renew the solution in order to avoid the accumulation of debris and contamination, which both decrease the detergent efficacy.

Implant surgical procedures expose patients, surgeons, and staff to potential cross-infections if carried out without a series of cleaning and sterilization procedures aimed at preventing the spread of pathogens. Bone drills are classified as critical surgical objects according to the classification proposed by E.H. Spaulding [25] and from the DMS dated 28/9/90 as instruments that come in contact with bleeding tissues and body fluids. For this reason, implantology drills must also be subjected to decontamination and cleaning procedures using chemical substances before proceeding to heat sterilization with saturated steam in an autoclave. All these procedures and protocols can alter the cutting efficiency, as well as deteriorate the depth marks printed on the drills, thereby altering the references that the surgeon has during surgery to check the working depth of the osteotomy. The reduction in cutting efficiency has considerable repercussions for the preparation of the implant site because a loss of sharpness and cutting efficiency of the drill results in a large part of the cutting energy being transformed into heat. The consequences manifest themselves as poor organization of the clot, delayed healing, and poor quality of the tissues that form at the bone–implant interface [18,26]. As reported previously in another study [18], implant osteotomy drills can be reused up to 50 times since their loss of sharpness is directly proportional to the number of osteotomies made.

Chemical detergents can cause metal corrosion with alteration of the cutting edge of the drill blades, which is a process that can worsen when the drills are submitted to saturated steam sterilization. In the literature, there are several articles that have studied the degree of wear of osteotomy drills in relation to their reuse [26,27]. On the other hand, there is no published work investigating the problem of chemical decontamination or metal release in the bone from surgical drills. In the present work, we chose to separately study the effect on bone drills of the two different chemical agents and the effect of autoclave sterilization in order to understand which of these aspects of bone instrument care is the most critical and potentially damaging to the drills.

We observed that all the disinfectants used were found to be potentially harmful to steel drills, causing corrosion zones that worsened after each decontamination cycle, while the zirconia drills did not show any structural damage, and the depth marks were preserved and remained clearly visible. No damage was observed for the steel and zirconia drills when they were only subjected to autoclave sterilization cycles. The results of the present study provide practical and valuable information that can help conserve the cutting efficiency of the drills by preventing metal release and overheating of the bone, both of which can increase the chances of implant failure [28].

Identifying factors and mechanisms with regards to implant failures should not be limited to the implants, but should also include the host and the drills. Drills are one of the main components of an implant procedure and play an important role in the success of an implant procedure [29,30]. Therefore, it is of primary importance to identify critical factors and develop appropriate therapies and prevention strategies. It is extremely useful to know the histopathology (macroscopic and microscopic aspects of the disease), the pathogenesis (source of the disease), and the physiopathology (mechanism of the disease) of the complications of implant failures, as well as changes in the structure of the bone drills during the processes of decontamination, cleaning, and sterilization.

From the results observed during this study, it is clear that the disinfectants used in clinical practice are potentially harmful to steel drills by contributing to corrosion of their surfaces and the loss of cutting efficiency.

#### **5. Conclusions**

The present study demonstrates that repeated immersions of steel drills in disinfecting chemical agents result in corrosion on the surface of steel drills. Conversely, these chemicals do not have any effect on zirconia ceramic drills, proving their inertness and structural stability, even in the harshest

environment. Autoclave sterilization cycles have no effect on any of the drills. Cleansing, sterilization, and maintenance of the drills are crucially important for patients' health and protection, but also for the drills' long-term durability and performance. It can be concluded that zirconia ceramic drills offer a surface that is not affected by disinfecting liquids. The fact that zirconia is immune to corrosion attack eliminates the possibility of the release of microparticles and ions in the peri-implant tissue during osteotomy, thus minimizing the chance of aseptic osteolysis [31].

**Author Contributions:** Conceptualization, A.S.; data curation, A.S.; formal analysis, S.N. and S.G.; investigation, A.S.; methodology, A.S.; project administration, A.S.; software, F.L. and P.S.; supervision, P.S.; F.I.; validation, A.S., S.N., F.I., and S.G.; visualization, P.S. and F.L.; writing—original draft, A.S.; writing—review and editing, S.N.

**Funding:** This research received no external funding.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## *Concept Paper* **A New Concept Compliant Platform with Spatial Mobility and Remote Actuation**

#### **Nicola Pio Belfiore**

Department of Engineering, University of Roma Tre, via della Vasca Navale 79, 00146 Rome, Italy; nicolapio.belfiore@uniroma3.it; Tel.: +39-06-5733-3316

Received: 27 June 2019; Accepted: 19 September 2019; Published: 21 September 2019

**Abstract:** This paper presents a new tendon-driven platform with spatial mobility. The system can be obtained as a monolithic structure, and its motion is based on the concept of selective compliance. The latter contributes also to optimizing the use of the material by avoiding parasitic deformations. The presented platform makes use of lumped compliance with three different kinds of elastic joints. An analysis of the platform mobility based on finite element analysis is provided together with an assembly mode analysis of the equivalent pseudo-rigid body mechanism. Surgical operations in laparoscopic environments are the natural fields of applications for this device.

**Keywords:** platform; spatial motion; remote actuation; cable actuation; laparoscopy; minimallyinvasive surgery

#### **1. Introduction**

A parallel architecture offers several advantages to the designers of spatial platform mechanisms. In fact, they rely on a multi-loop topology that is certainly convenient for the stage stiffness and accuracy, whereas their forward kinematic analysis becomes more complex.

The Stewart–Gough platform, a mechanism that can be considered to be a milestone of parallel manipulators, was presented in 1965 [1]. This six-DoF (degree of freedom) system can be controlled in any combination by six motors and has the advantage of no fixed axis relative to the ground. Classical issues for parallel manipulators have been extensively studied in the literature, such as structural kinematics [2], workspace [3], singularity [4], optimal design [5], structure synthesis [6], manipulability [7], control of redundantly-actuated [8], and remotely cable-driven parallel manipulators [9]. On the other hand, more recent subjects have still not been well investigated for parallel platforms, such as connectivity and redundancy [10], topology [11], and planarity [12].

Classical parallel platforms are composed of rigid links and ordinary kinematic pairs with a geometric closure configuration. However, they could be built as compliant mechanisms [13–15], which present a series of advantageous characteristics: they are not subject to backlash and do not need lubrication; they can be also built from a unique block of material; and finally, they have generally a neutral or balance configuration from which the deformed poses can be achieved. In fact, they can reach a given configuration thanks to external forces that can be applied with a high precision to deform the elastic structure, using also a redundant driving strategy. More recently, active compliance [16,17] has been added as a further possibility in design, acting both as a series or in a parallel configuration with passive compliance.

These features make compliant mechanisms very interesting for applications where lubrication is impossible or where extreme accuracy is needed. For these reasons, a group multi-DoF compliant stages has also been developed in literature [18].

Since 1990, stiffness and conditioning maps of the workspace of parallel manipulators have been established [19], in order to prevent special types of singularities, which result in a loss of controllability. A six-DoF force sensor was designed in 1991 [20] on the base of the Stewart–Gough platform. In this layout, the fixed and mobile platforms are coupled by six spring-loaded pistons, whereas the length variations are measured by means of six linear voltage differential transformers mounted along the pistons. The Stewart–Gough inverse and forward kinematic transformations are used to calculate the forces and torques that are applied to the mobile platform. A three DoF translational compliant parallel platform was presented in 2005 [21] for nanomanipulation. Workspace, dexterity, and isotropic configurations were studied by using the pseudo rigid-body model (PRBM). A six-PSS (prismatic-spherical-spherical) nanopositioner compliant mechanism was designed [22] to be actuated by means of six multilayered piezoelectric actuators. The system is composed of one fixed plate, three two-PSS compliant mechanisms, and one end effector. The PRBM is also used in this investigation to study its kinematic analysis. A three DoF spatial translational accurate positioning compliant platform with flexible hinges and with piezoelectric actuators has been designed [23] to achieve high stiffness, a high speed of dynamic response, high kinematic accuracy, and high resolution. A six-DoF compliant parallel micro-scale manipulator with piezo-driven actuators and integrated force sensor has been designed [24] to provide real-time force information for feedback control. Kinematic and static analysis were investigated to achieve high positioning accuracy, compactness, and smooth and continuous displacements. A method for the optimal design and performance characterization of micromanipulators has been also applied to six-DOF parallel micromanipulators [25]. A three-DoF compliant platform has been studied [26] to make it able to move in three-dimensional space. The system was composed of compliant joints, actuators, and a central moving platform. The actuators consisted of three binary links, while the moving platform was an equilateral plate. The free end of each actuator and the central platform were connected by springs in such a way that the motion of the actuators was transmitted to the moving platform. Considering the applications at the micro scale and using the technology on which micro electro-mechanical systems (MEMS) are based, a compliant three-DoF plane parallel platform has been proposed [27] together with its kinetostatic optimization.

The "da Vinci" c surgical robot (by Intuitive Surgical, Inc., Sunnyvale, California, USA) is a widely-used system designed to facilitate surgical operations with a minimally-invasive approach. This robot makes use of multi-DoF end terminals as a resource to cope with different tasks, working in cooperation with robotic wrists or steerable instruments, and their characteristics have been extensively improved and refined throughout the years. For example, a 2 mm-diameter instrument equipped with a three-DoF wrist has been investigated and tested [28] for the robotic "da Vinci" platform. Moreover, new systems for measuring the end effector gripping force have also been developed by means of a torque transfer system [29]. Finally, deflection and force feedback from the "da Vinci" end effector have been provided by new types of strain gauges [30].

However, in most of the above-mentioned systems for remote manipulations that are widely adopted for minimally-invasive surgery, the wrists and end effector consist of mechanisms that have ordinary kinematic pairs, which are subject to backlash problems, and a serial kinematic structure, which is usually less robust than a parallel structure. The present paper presents a new six-DoF platform for remote manipulation that consists pf a mechanism with selective compliance (compliant mechanism) and has also a parallel structure. The device could be either part of "da Vinci" or independently driven by another positioning system. Originally, the system was conceived to work under a laparoscopic environment, and it is expected to improve its success in surgery, such as in laparoscopic sleeve gastrectomy (LSG) with cruroplasty [31], in surgical treatment of gastrointestinal stromal tumors of the duodenum [32], in colovesical fistula surgery with a minimally-invasive approach [33], in endoluminal loco-regional resection by transanal endoscopic microsurgery (TEM) [34–36], and also in low rectal anterior resection (LAR) [37].

#### **2. Description of the New Concept Platform**

In several applications, the position of a mobile platform in space has to be controlled by using remote means, such as cables. Usually, the conventional mechanisms that are able to implement such a feature are rather complicated because the platform has six degrees of freedom (DoF), and moreover, they are subject to backlash and parasitic deformations. This problem is quite general, but in this paper, a specific implementation suitable for surgical applications will be presented.

A new tendon-driven compliant mechanism is herein proposed, as a possible solution to the above-mentioned problem. The full mobility of the platform in space and, in particular, its raising motion is possible because of a new elastic joint, which combines the action of an elastic curved beam and of a portion of the conjugate surfaces. The invention consists basically of a wire-operated selective compliance mobile platform like the one represented in Figure 1. The mechanism base (k) is intended to be mounted on the end of a flexible tubular duct for endoscopic, surgical, therapeutic, or diagnostic uses.

**Figure 1.** A view of the compliant platform and of all its elements: platform (**a**); plaform hole (**b**); type *S* elastic joints (**c**); type-U elastic joints (**e**); upper (**d**) and lower (**g**) links; upper (**f**) and lower cables (**i**); conjugate surface flexure hinge (CSFH) hinges (**h**); base link (**k**).

The platform (a) is designed for supporting surgical means, normally used during endoluminal operations, such as vision systems, forceps, scissors, cannulae, electrotomes, and so on. However, the system could be used for precision applications or in adverse environments, e.g., for operations in the aerospace environment. The base (k) and the platform (a) are connected through a plurality of legs, which provide mobility in space to the mobile surface (a), and are operated by actuating wires (i) and (f), running inside the tubular duct, to control and operate the platform remotely.

Since the mechanical structure of the mechanism is based on selective compliance and, particularly, on lumped compliance, there is a neutral configuration that is assumed when no external force is acting on the structure.

#### *2.1. Deduction of the Pseudo-Rigid Body Equivalent Mechanism*

A compliant mechanism can be generally modeled as its equivalent so-called pseudo-rigid body mechanism (PRBM). The PRBM is a mechanism with only ordinary kinematic pairs, which presents approximately the same motion as the original compliant mechanism in the neighborhood of the neutral configuration. For this purpose, each elastic joint is replaced by an ordinary kinematic pair, which can offer mobility that is compatible with the selective compliance characteristics of that

elastic joint. Figure 2 shows the original compliant mechanism (Figure 2a) and its corresponding spatial PRBM (Figure 2b).

**Figure 2.** The compliant platform (**a**) and its corresponding pseudo-rigid body mechanism (**b**), with the equivalent revolute joints R, spherical joints S, prismatic pairs P, a triple spherical joint *S*3, and the cable directions *ξ*1, *ξ*2, and *ξ*3.

With reference to Figures 1 and 2, the elastic joints can be distinguished according to the following characteristics.


with a very good accuracy, because of the presence of a portion of conjugate surfaces. Therefore, they are replaced by classical revolute joints R.


Three linear actuators *SPS* are added to the system and positioned as in Figure 2b in order to replace the three actuated cables directed along the *ξ*1, *ξ*2, and *ξ*<sup>3</sup> directions. The three linear actuators are identified in the figure as the ones that are incident to the triple spherical joint *S*<sup>3</sup> positioned at Point B. This replacement is justified by the fact that the three cables are directed along lines that pass through the center *B*of the triple spherical joint *S*3. This point is positioned in the middle of the fixed platform, in correspondence to a level that does not interfere with the CSFH hinges.

Finally, it is worth noting that the identification of a PRBM that adequately corresponds to the proposed compliant structure represents the first necessary step to further analyze the new systems, such as workspace and kinematic analysis, kinematic synthesis, and kinetostatic behavior.

#### *2.2. Topological Analysis*

Considering an equivalent mechanism PRBM with rigid bodies and classical U, S, and R pairs, three legs guarantee six degrees of freedom to the platform. In fact, the PRBM presents - = 8 rigid links and *m* = 9 kinematic pairs. In case Type (e) joints are replaced by U joints, the structure will be composed of three Type (h) revolute joints R with degree of constraint *ci* = 5 in space, three Type (e) U joints with *ci* = 4, and six S joints with *ci* = 3. Therefore, according to the general topological Grubler's formula, the PRBM has:

$$F = \lambda \left(\ell - 1\right) - \sum\_{i=1}^{m} c\_i = 6\left(8 - 1\right) - 3\cdot 5 - 3\cdot 3 - 3\cdot 4 = 6\tag{1}$$

overall degrees of freedom (DoF), where *λ* = 6 is the mobility number for general spatial motion.

As mentioned above, torsion cannot always be excluded on U elastic Type (e) joints, depending on the minimum diameter of the normal cross-section, which would make them practically equivalent to S joints. In this case, Grubler's formula would yield *F* = 9 DoFs for the platform, but it must be remarked that three of such DoFs would be uniquely dedicated to providing idle rotations to the upper Type (d) links. In this case, any Link (d) would be connected to the remaining parts of the structure by means of two S type pairs, and so, rotations about an axis passing through the centers of the two spherical joints would be possible. These rotations are naturally counterbalanced by internal elastic reactions that would drive the system back toward the minimum of the potential elastic energy. Alternatively, they could make it easier to achieve an optimal attitude of Type (f) cables that pull down Type (d) links. For these reasons, a different manipulator could be obtained, as an alternative, where Type (e) links are replaced by Type (c) links, with no problems for mobility.

According to the result obtained by using Equation (1) and considering that each leg is supposed to be controlled by two cables, a three-legged platform will be the one that has a number of independent actuators that is equal to the number of DoF and therefore will be considered as an optimal choice for the compliant structure. In fact, according to the principle of selective compliance, any elastic element where compliance is concentrated presents a peculiar geometry that is intended for a specific deformation, for example a prescribed flexion or torsion axis, and all the deformations different from the prescribed ones are considered to be as parasitic deformations, because they do not contribute to the desired motion, but only increase the stress level in the elastic material. For this reason, a satisfying geometry of a compliant mechanism is the one that minimizes the parasitic deformations.

#### *2.3. Direct Position Analysis*

Thanks to the construction of the PRBM depicted in Figure 2b, it is possible to identify some fundamental characteristics of the platform, as they have been introduced in the literature. For example, it is clear that this platform is not a fully-parallel platform, because two DoF are needed for each leg. With reference to Figure 3a, the *i*th leg (with *i* = 1, ... , 0) will be composed of the pseudo rigid links *CiAi* and *AiPi*, which respectively correspond to Type (g) and Type (d) links of the original compliant structure.

**Figure 3.** (**a**) The circles Γ*Ei* and Γ*<sup>i</sup>* as loci of points *Ei* and *Pi*, respectively, for the *i*th leg; (**b**) the virtual bar *QiPi* rotating along the axis *wi* parallel to the line *AiB*.

For the generic *i*th leg, one DoF is firstly required to define the angular position of Type (g) link *CiAi*. An angle *α<sup>i</sup>* can be introduced to measure the rotation of (*CiAi*) with respect to its position in the undeformed configuration of the CSFH joint. Since the latter corresponds to a revolute joint with a known rotation axis, the angle *α<sup>i</sup>* uniquely identifies the position of the center *Ai* of the spherical pair. Secondly, another DoF is needed to assess the position of the upper Type (d) *AiPi* link of the *i*th leg. Indeed, an assigned pull command on the Type (f) cable has the effect of bringing points *Ei* and *B* closer to each other. This effect could be similarly obtained by introducing in the PRBM a virtual linear actuator being active along the line *BEi*. Any contraction of the linear actuator *BEi* corresponds to a pull command of the (f) rope, while an extension of the linear actuator would represent a reduction of the cable tension. Since mobility is granted by the elasticity of the structure, its overall configuration will depend on the whole set of tensions that are assigned to the six cables. Furthermore, it is worth noticing that positive tensions (push) are not considered here, and therefore, the maximum elongation of the three virtual linear actuators will depend on the whole balance between the tensions that are applied to the cables and the structural elasticity. For the linear actuator *BEi*, the pulled distance *di* can be introduced as the shortening of the original length |*BEi*| with respect to the distance between points *B* and *Ei* in the undeformed structure configuration.

Once the input parameters *α<sup>i</sup>* and *di* have been assigned, the chain *BAiEi* behaves as a rigid structure, which may rotate about the axis *wi* passing through points *Ai* and *B* (see Figure 3b). Therefore, point *Ei* describes a circle Γ*Ei* laying on a plane *πHi* that is orthogonal to *wi* and whose

center *Hi* is on line *wi*. Since *AiPi* can be regarded as a rigid link, point *Pi* is also forced to lay on a circle Γ*<sup>i</sup>* that lays on a plane *πQi* parallel to *πHi* . The center *Qi* of Γ*<sup>i</sup>* is on the line *wi*.

Considering the three loci Γ*<sup>i</sup>* (with *i* = 1, ... , 3) of the possible positions of the points *Pi*, it is clear that three points of the upper platform, coincident with *P*1, *P*2, and *P*3, will belong to the three circles Γ1, Γ2, and Γ3, respectively. However, exactly the same constraint could be imposed by introducing a virtual link *QiPi*, represented in Figure 3b, that rotates about the *wi* axis. Therefore, three new links *QiPi*, with *i* = 1, ... , 3, can be used to get rid of the three whole chains made of links *CiAi*, *AiPi*, and the linear actuators *BEi*. After this substitution, a new three-legged structure is obtained, as depicted in Figure 4.

**Figure 4.** The reduced parallel structure: points *Qi*, axes *wi* and points *Pi*.

The new mechanism will have a null DoF because the whole set of input positions has already been assigned. In fact, after assigning a value to the three angles *α<sup>i</sup>* and to the three displacements *di*, the axes *wi*, the lengths |*QiPi*|, and the positions of points *Qi* can be uniquely identified. The resulting structure consists of a mobile platform that is connected to the base via three links only arranged in a parallel configuration, each one having one revolute R and one spherical S joint at its ends incident to the base and the platform, respectively. This structure has received the attention of several eminent scholars in the field and has been extensively studied [52–54]. From the geometric and kinematic point of view, the study of the possible assembly modes of this zero-DoF structure gives the same solution as for problem of finding the assembly modes of a six-DoF, so called 6-3-type fully-parallel mechanism, belonging to the class of Stewart platform mechanisms, once six elongation values are assigned to the six linear actuators along its legs.

Innocenti and Parenti Castelli solved the direct position analysis in 1990 [55] and found results that were coherent with Hunt's works [2]. According to this method (see also [56]), three closed-loop vector equations:

$$\begin{aligned} \overrightarrow{P\_1P\_2} &= -\overrightarrow{Q\_1P\_1} - \overrightarrow{P\_2Q\_2} - \overrightarrow{Q\_2Q\_1} \\ \overrightarrow{P\_2P\_3} &= -\overrightarrow{Q\_2P\_2} - \overrightarrow{P\_3Q\_3} - \overrightarrow{Q\_3Q\_2} \\ \overrightarrow{P\_3P\_1} &= -\overrightarrow{Q\_3P\_3} - \overrightarrow{P\_1Q\_1} - \overrightarrow{Q\_3Q\_1} \end{aligned} \tag{2}$$

can be written, where −−→*P*1*P*2, −−→*P*2*P*3, and −−→*P*3*P*<sup>1</sup> are the edges of the upper platform.

For the sake of the present investigation −−→*P*1*P*2, −−→*P*2*P*3, and −−→*P*3*P*<sup>1</sup> have constant modules because of the symmetry of the upper platform. Therefore, given the constant length *l* of the upper platform edges, Equation (2) can be rewritten as:

$$
\overrightarrow{P\_1P\_2} \cdot \overrightarrow{P\_1P\_2} = l^2 \, \,, \qquad \overrightarrow{P\_2P\_3} \cdot \overrightarrow{P\_2P\_3} = l^2 \, \,, \qquad \overrightarrow{P\_3P\_1} \cdot \overrightarrow{P\_3P\_1} = l^2 \, \, \tag{3}
$$

from which three scalar conditions are obtained where the three unknown are the rotation angles *θ<sup>i</sup>* (with *i* = 1, . . . , 3) of the virtual bars *QiPi* around the axes *wi*.

It is now essential to remind that once the three rotations *α<sup>i</sup>* of the CSFHs and the three displacements *di* of the Type (f) cables have been assigned, the zero-DoF structure illustrated in Figure 4 is completely configured because the positions of the points *Ai*, *Hi*, and *Qi* can be easily calculated. Therefore, the solutions of the problem expressed by the set of Equation (3) are also the solution of the assembly configuration for the PRBM mechanism depicted in Figure 3a.

The system (3) consists of three second-order algebraic equations in three unknowns *θ<sup>i</sup>* (with *i* = 1, . . . , 3), where any equation contains two unknown variables only. Therefore, the solutions can be achieved by firstly eliminating one variable ˆ *θ* from two equations where ˆ *θ* appears, so obtaining one equation in the other two variables, and then, by eliminating one of the other two variables, say ˜ *θ*, from the remaining two equations. The result is a 16th-order polynomial equation in the remaining variable *θ*, with 16 real and complex solutions for *θ*. Since for every solution *θ*, unique values of ˆ *θ* and ˜ *θ* exist, a unique location of the upper platform is identified for each solution *θ*. These solutions correspond to the possible assembly configurations of the structure represented in Figure 4 and, as a consequence, of the PRBM depicted in Figure 3a, provided that the six inputs *α<sup>i</sup>* and *di* have been assigned. However, for the sake of the present investigation, the only interesting solution will be the one compatible with rotations and displacements starting from the initial undeformed configuration represented in Figure 2a. This shows that the numerical approaches could be used more conveniently than the purely analytical ones, because they could converge to the actual configuration by using the undeformed pose as the starting guess. In the next section, finite element analysis (FEA) is applied to the compliant platform illustrated in Figure 2a, by assigning three different sets of input displacements.

#### **3. Numerical Simulation of the Platform Pose**

The peculiar geometry illustrated in Figure 1 is the result of a preliminary study that led to the definition of the patented structure. Three equal legs were positioned in a parallel configuration, each leg being actuated by two cables, and so, the whole structure was a tendon-driven mechanism. The geometry of each leg was chosen in such a way that the lower and upper cables induced a raising and lowering motion, respectively. The attachment points were also selected in order not to induce cable jamming. Further optimization of the attachment points and of the angles of the pseudo-rigid links will be the object of future investigations. Considering the nomenclature introduced in Figure 1, any moving cable (i) acts on a CSFH turning pair, relevantly operates the bending of the CSFH Type (h) flexure, and actually drives the rotations of Type (g) links. Cables (f) will have the effect of pulling the platform down because they are attached to the upper links. More in general, a configuration of the platform (a) will be defined by the whole set of forces applied to all the wires, since it depends on the interaction between the applied forces and the elasticity of joints.

Finite element analysis is a convenient way to assess the deformation of the whole structure for assigned values of the cable displacements. More specifically, FEA provided evidence that the adoption of the proposed platform can be a promising approach to find an efficient way for remote handling in several contexts.

#### *Finite Element Analysis*

Finite element analyses were conducted to evaluate the static behavior of the parallel platform. Three cases were considered depending on three different sets of input parameters and using *<sup>E</sup>* = 1.1 · 109 Pa as the material Young's modulus.

Three cases will be studied:


The fixed reference frame (*x*, *y*, *z*) and the unit vectors (*ux*,*uy*,*uz*) attached to the mobile platform were positioned as in Figure 5a. This figure also shows the input displacement *d*1. Rotations *θx*, *θy*, and *θ<sup>z</sup>* were assumed to be about *ux*, *uy*, and *uz*, respectively.

In the first case, a displacement was imposed on each one of the Type (f) cables, equal to *d*<sup>1</sup> = *d*<sup>2</sup> = *d*<sup>3</sup> = 0.5 mm, and null tensions on Type (i) cables, giving rise to null rotation angles *α*<sup>1</sup> = *α*<sup>2</sup> = *α*<sup>3</sup> = 0 of the three CSFH hinges. The deformed configuration is reported in Figure 5b, showing a platform displacement along the *z*-axis in the negative direction. No other significant displacements or rotations were registered.

The second case corresponded to *α*<sup>1</sup> = *α*<sup>2</sup> = *α*<sup>3</sup> = 20◦ with *d*<sup>1</sup> = *d*<sup>2</sup> = *d*<sup>3</sup> = 0 mm. The deformed configuration is reported in Figure 6a, showing a platform displacement along the *z*-axis in the positive direction. Analogous to the previous case, no other significant displacements or rotations were registered.

The third case corresponded to a general actuation scheme with *α*<sup>1</sup> = 0◦, *α*<sup>2</sup> = 5◦, *α*<sup>3</sup> = 20◦, *d*<sup>1</sup> = 1 mm, *d*<sup>2</sup> = *d*<sup>3</sup> = 0 mm. The deformed configuration is reported in Figure 6b, showing a platform displacement with components along the *x*− and *y*-axes and rotations about the *x*- and *z*-axes.

The input parameters, the platform displacement, and the rotations are reported in Table 1 for the three analyzed cases.

**Figure 5.** (**a**) Reference frames and nomenclature; (**b**) platform displacement along the *z*-axis, negative direction (Case 1).

**Figure 6.** (**a**) Platform displacement along the *z*-axis, positive direction (Case 2); (**b**) platform pose for a generic actuation scheme (Case 3).

**Table 1.** Input rotations and displacements and their effect on the platform for the three analyzed cases.


#### **4. Applications**

Originally, the main activities for the invention herein presented were intended to be operated in the laparoscopic environment. Figure 7 shows a possible end-effector that could be mounted on the platform. With reference to the labels used in Figure 7, the endoluminal catheter (a) carries the base platform (b), which supports three Type (c) legs on which the mobile platform (d) is mounted. The mobile platform surface holds the surgical means (f) that can vary according to the type of required operation. Other miniaturized instruments can be mounted on the controlled platform, such as vision means (e) that allow the surgeon to observe the corporal cavity wherein the device is inserted. Moreover, a communication duct (g) was designed, allowing the surgeon to access the region to be operated. For this reason, the mobile and base platforms were also provided with an opening that connects the duct (g) with the tubular duct (a). With reference to Figure 7, it should be also noted that the surgical device was comprised of a shaped surface (f) that made it easier to act as a guiding element inside the cavity during the use of the device.

**Figure 7.** A view of an end-effector mounted in the platform: catheter (**a**); base link (**b**); legs (**c**); platform (**d**); on-board hardware (**e**); on-board end-effectors (**f**) and (**g**).

#### **5. Discussion**

The aim of this paper was to present a new concept high accuracy platform with spatial mobility, remotely actuated, and equipped with selective compliance joints. The system can be built on a unique material block or with a reduced number of components, which reduces the costs and time of production. It can be also built by means of 3D printing.

The platform was mounted on three arms, and it was remotely controlled by six wires. The system included a mobile plane and a connection base fixed to an endoscopic instrument. The instruments was accurate and maneuverable with continuous motion granted by the interaction between the cable tensions and the elastic energy stored in the elastic media. Based on selective compliance, the principle of design gave rise to optimal configurations where parasitic motions, friction, and wear were minimized. No lubrication was needed.

The invention is expected to drive surgical operations in laparoscopic, endogastric, or endarterial environments, but other applications are not excluded, such as in aerospace, automotive, appliances, and microelectronics. However, it is worth noting that the platform fabrication and its actual implementation for real operations deserve further refinements, and therefore, they will be treated in future contributions. Among the important subjects that still represent open problems, the following will be briefly addressed.

The first problem is the selection of an optimal material for the elastic parallel mechanism. This choice will depend on the overall size of the device and on the consequent preferred method of machining. In any case, some desired characteristics of a material that could be conveniently employed to build a compliant mechanism block were proposed in [57], among which are good performances at variable temperatures, biocompatibility, low susceptibility to creep, resistance to wear and fatigue, and the predictability of such properties. However, the most important characteristic is a high value of the ratio of the yield strength to Young's modulus. According to Table 2.1. presented in [57], there are several materials that have an acceptable ratio, among which are nylon, e-glass, Kevlar, and polyethylene.

The actual fabrication of the device will depend both on size and material. Unfortunately, the geometry is rather complicated, and so, many of the classical machining operations would be problematic.

The identification of a proper PRBM, as proposed in the present contribution, could be helpful to complete typical tasks in robotics, such as the study of the critical configurations. Furthermore, the PRBM will be useful to optimize the platform and the legs' geometry, in order to suit the required workspace, mobility, and mechanical advantage.

Finally, an efficient control algorithm would be required for each specific application.

#### **6. Conclusions**

A spatial, selective compliance, tendon-driven, and parallel platform was described and analyzed. This system was quite different from the compliant mechanisms previously presented either in the literature or the national patent institutions until today. Its mechanical structure was studied by identifying the equivalent pseudo-rigid body mechanism. The platform was also simulated with finite element analysis (FEA) by assigning different sets of cable tensions and obtaining results that matched well with the expected behavior. It is hoped that this article will offer new perspectives for general tasks of spatial body guidance and particularly in laparoscopic surgery.

#### **7. Patents**

The following patents describe the new concept platform and the related claims.


#### **Funding:** This research received no external funding.

**Acknowledgments:** The whole staff of the "Research and Technology Transfer Area" of the University of Rome la Sapienza is gratefully acknowledged. Particular thanks go to the Manager of the "Research and Technology Transfer Area" Antonella Cammisa, the Office Manager of the "Enhancement and Technology Transfer Office" Daniele Riccioni, and the Office Manager of the "Grant Office" Alessandra Intraversato, for their counseling and support during my long stay at Sapienza University. I am also grateful to several people from my new University of Roma Tre (my list would be too long to mention all of them) for supporting and encouraging me since my arrival in October 2017.

**Conflicts of Interest:** The author declares no conflict of interest.

#### **Abbreviations**

The following abbreviations are used in this manuscript:


#### **References**


c 2019 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
