*Proceedings* **Design of a Hybrid Two-Degree-of-Freedom Lower Limb Exerciser** †

## **Daniel Lates, 1,\*, Laura Irina Vlas,in <sup>2</sup> and Alexandru Ianos,i-Andreeva-Dimitrova <sup>2</sup>**


Published: 16 December 2020

**Abstract:** Lower limb rehabilitation is an often-encountered need. This paper presents the design process of an exerciser that combines robot-assisted physiotherapy with functional electrical stimulation (FES) of the lower limb muscles. The exerciser features two degrees of freedom, one focuses on the rehabilitation of the muscles responsible for dorsiflexion and plantar flexion, the other one on the muscles responsible for the inversion and eversion of the foot. These motions might be accompanied by FES, if the physiotherapist so recommends. The presented exerciser constitutes a mechatronic device that seamlessly integrates mechanical design, electronics and control engineering.

**Keywords:** rehabilitation engineering; medical robotics; lower limb rehabilitation

## **1. Introduction**

Lower limb rehabilitation is a subject which, among rehabilitation engineers, is not as popular as upper limb rehabilitation. A simple search query with the keywords "lower limb rehabilitation robot" returns less than half the results for the keywords "upper limb rehabilitation robot" on the popular science platform PubMed. This disparity can be explained by the fact that designing for the upper limb is more challenging from a technical point of view than designing for the lower limb, and consequently more palatable, yet there are many more situations that necessitate the rehabilitation of the lower limb (e.g., prolonged inactivity due to a certain illness impacts much more the lower limb). Lower limb orthoses are used to support the foot in a certain position and assist in recovery of gait; they are also used to redistribute forces that occur when the foot comes in contact with the ground while walking so as not to exert too much force on a specific affected area of the foot [1,2]. A robotized exerciser empowers a physiotherapist by providing a tool for repeatable and reproducible results, enabling more efficient and targeted procedures; moreover, provided the exerciser is affordable and meant to be also used in non-clinical environments, it facilitates rehabilitation for the patient in a prescribed way.

This paper describe the critical milestones in the design of a two-degree-of-freedom (DOF) hybrid lower limb exerciser [3]; the hybrid part is given by the fact that it combines the traditional physiotherapy assisted robotically with the functional electrical stimulation (FES) of the relevant muscle groups. The exerciser focuses on the ankle joint, namely, the dorsiflexion/plantar flexion and the inversion/eversion of the foot. The designed exerciser does not mandate the usage of FES in conjunction with the robotically assisted physiotherapy, it merely provides the option of simultaneously usage. The paper provides a description of the state of the art, after which it focuses on the mechanical design and describes the electronics and coding involved in the control of the proposed exerciser.

#### **2. State of the Art**

In this chapter several examples of rehabilitation equipment will be discussed that are in accordance with the object of the paper and which are considered representative.

In his patent [4], Stein presents an electronic stimulator with fixed electrodes attached to a textile tape. This band must be positioned correctly on the leg so that the electrodes are placed in an area over the nerve to be stimulated. The band also contains devices for monitoring body movement and a system that operates the electrodes at certain intervals to stimulate the nerve and activate latent muscles. This device can be used in the case of a person who suffers from "drop-foot" that may occur as a result of a stroke.

Gil et al. [5] describe a unilateral hybrid orthosis-type exoskeleton intended to assist and recover gait for patients who experience motor deficiencies due to central nervous system diseases. It consists of an orthosis at the knee, ankle and foot that supports the lower limb and a functional electrical stimulator that activates the affected muscles. The support part has the role of constraining the ankle and knee joint and stopping their involuntary movements in certain directions. This ensures a stable position of the lower limb while walking and while the patient is standing.

A platform presented by Liu et al. [6] is intended for patients who have suffered a stroke and experience motor deficiencies as a result. In order to recover the functions of the lower limbs, therapy based on exercises is needed, which has the role of strengthening the muscles and correcting the position of the leg. The device proposed in this example assists the patient in performing certain exercises that improve the ability to move the foot. The robotic platform consists of two symmetrical plates that have the role of foot support, each with 3 DOF and can perform internal and external rotation of the ankle, dorsal and plantar flexion and inversion and eversion of the foot. The patient can use the device in three ways depending on the rehabilitation stage: exercises that involve maintaining a constant speed, exercises that keep the motor speed constant and exercises that involve the proactive involvement of the patient in training.

Erhan and Mehmet [7] elaborate a study on the design and control of a robot for therapeutic exercises for the lower limbs of a patient who needs rehabilitation after a spinal cord injury. To control this robot, a "human–machine interface" with a rules-based control structure was developed. The robot manipulator can perform active and passive exercises, as well as learn specific exercise movements and perform them without the physiotherapist through the human–machine interface. Moreover, if a patient reacts against the robotic manipulator during an exercise, he may change position depending on the feedback data.

An interesting application of orthosis is the ability to assist the transfer from a sitting position to a standing one; Aroche et al. [8] proposed a computerized system for persons that suffer from complete paraplegia, arguing that widespread adoption of powered orthosis among this demographic is hampered by the fact that these orthoses does not provide equilibrium autonomy. Another system [9] blocks all but one DOF of the lower limb and makes use of mechanical linkages and automation for independent locomotion; it is not entirely clear if it can also provide the transfer function. Roula et al. [10] compared multiple operating conditions and concluded that PID controller might not perform well enough due to various uncertainties presented by the complex interaction between a subject, their orthosis and the environment.

#### **3. Design Process**

From a structural standpoint, the designed exerciser is composed of three interconnected subsystems that are detailed in the following paragraphs. The integration of these parts makes the device a mechatronic product.

#### *3.1. Mechanical Subsystem*

The mechanical subsystem is designed to enable movement only in a predictive fashion; for a correctly executed exercise, a proper attachment to the foot is necessary that lines the bones, muscles, and tendons in an anatomically appropriate way. In order to achieve this goal, biomechanical data were taken into account, namely, it was hypothesized that the exerciser is used by a person 1.65 m tall with a mass of 50 kg; this gives a weight of the foot of 7.13 N and a position of the center of gravity (CG) by the following coordinates in relationship to the heel: 0.098 m horizontally and 0.039 m vertically (Figure 1a). The range of movement of the foot in relationship to the transverse plane allowed by the exerciser is −35◦; 20◦ for the plantar flexion/dorsiflexion; −20◦ and 15◦ for inversion and eversion, respectively. Given these data and using the geometrical relationship between the foot CG and the designed mechanism (Figure 1b), the result is a maximum necessary moment of 0.37 Nm for the first DOF, and 0.27 Nm for the latter.

**Figure 1.** Input biomechanical data: (**a**) range of motion and position of the center of gravity of the foot (**b**) geometrical relationship between the center of gravity and exerciser.

The employed mechanism is a spatially stacked version of the well-known four bar linkage. Its main purpose is to provide a way of simultaneously actuating both degrees of freedom; 4 four-bar linkages are connected to form a parallelepiped, each vertex being formed out of two rotational joints, their axes perpendicular to each other and parallel to the other 3 sister joints axes (Figure 2a). The placement of a motor in one of the joints is trivial for actuating one DOF, but the second actuated DOF (Figure 2b dotted line) raises additional issues, as the linkage has to be connected to a fixed reference; if directly connected, the whole DOF is pinned. The designed solution was to incorporate in the power train an universal joint coupled to a sliding shaft with parallel splines; this allows the necessary tilt angle as well as accounting for the radial displacement. Due to the fact that the mobile part of the exerciser has considerable mass, additional support mechanism is employed: two gas cylinders, their ends connected by spherical joints add stability to the system (drawn with red on Figure 2c).

Referring to the aforementioned figure, the immovable part (drawn with blue) is attached to the leg by Velcro straps, which are not pictured, as to not overload the schematic. The foot is resting on a specifically designated platform. The design is modular, so that the footrest is easily changeable to accommodate various feet sizes by removing and reinserting the bottom U-shape shaft (drawn in magenta on Figure 2c). The normal operation of the exerciser presumed oscillatory movement, therefore the design does incorporate only plain bearings; the friction is dealt by using polytetrafluoroethylene bushing, the low speed nature of the real life use case scenario allowing sufficient time for cooling. The CAD model was designed using SolidWorks software package published by Dassault Systèmes.

**Figure 2.** Design stages of the lower limb exerciser: (**a**) kinematic chain (**b**) mechanism, where FR is the foot resting plate, Y is the yoke, with 1 are designated the vertical linkages (0.330 m) and with 2—the horizontal linkages (0.143 m); dotted line represents the rotational axis (**c**) CAD model of the exerciser.

#### *3.2. Electronics Subsystem*

The electronics subsystem is built around an ATmega328-P microcontroller (refer to Figure 3a) that commands the actuation of the mechanical subsystem with two electrical motors, each powered by an H-bridge. Each electrical motor is encapsulated with a 210:1 gear ratio transmission, capable of delivering up to 3 Nm of torque, which is well above the computed necessary. The H-bridge is compatible with PWM signals and also provides a quick response disable input. The angular positioning of each DOF is monitored with a resistive absolute encoder that provides an accuracy of ±0.3◦. For additional safety, each DOF has 2 normally-closed limit switches, each of them controlling a normally-open relay in such a manner that if one of the limit switches is tripped, or the power to the switches is somehow interrupted (rusted connection, torn wire, etc.) only one direction is stopped; therefore, recovery of the system is still possible in normal operation and a high standard of safety is employed. Each faulty state is signaled to the microcontroller galvanically insulated through an optocoupler that drives the first interrupt pin to which an interrupt routine is attached.

**Figure 3.** Electronics subsystem: (**a**) System architecture, where LS are limit switches, RE—resistive encoder, SD–SD read/write module, UU–USB to UART converter, H–H-bridge, M—motors, R—relays, FES—functional electrical stimulation unit and μC—the microcontroller; (**b**) PCB layout.

An SD-card module is included which allows for upload of different exercises; the file is a simple text string, each row containing one command that contain the desired position and maximum allowable speed for each motor as well as the necessary commands for the start/stop of FES system. The FES system used by the exerciser is a commercially available 2-channel device interfaced with by

relay; therefore, the pulse length, frequency and amplitude of the stimulation is manually dialed in before commencing the exercise, the microcontroller merely starts or stops the device. The placement for the FES electrodes on the skin is covered by the device user manual and might be performed either by a physical therapist or the patient after receiving a precursory instruction. The exerciser's main electrical circuit was implemented on a single layer printed circuit board (PCB), pictured in Figure 3b, using EAGLE (published by Autodesk); it is worth noting that this PCB is not entirely necessary if an Arduino board were to be used. Furthermore, for programming as well as testing purposes, communication over a USB to UART converter is employed.

## *3.3. Control Subsystem*

ATmega328-P microcontroller is a popular microchip with the Arduino device family; therefore, the Arduino IDE was used in code design for its easy-to-use libraries. The motors were controlled using a PID algorithm implementation which reads the signal from the resistive absolute encoders through the microcontroller integrated 10-bit ADC and compares it to the target position provided by the exercise file that resides on the SD-card. The output from the PID controller is a PWM value that is proportionally to the motors speed; it is worth noting that if the value is negative, which correlate with the rotation in the opposite direction, a simple function remove the sign and invert the signal before further processing. The sign triggers a flag that signalize the H-bridge which combination is active, so that the motor can easily turn. In order to limit the speed in a safe range, the PWM value is capped before writing it in the appropriate PWM register with the value specified in the exercise file. The overall safely usage of the exerciser is ensured by the hardwired limiters described in the precedent subchapter, but as a first line of secure operation there are also software-defined limits which maintain a physiological range of motion.

Another mode of operation is by permanent connection via an USB-UART converter. At this stage a simple graphical user interface was designed in Matlab GUIDE, but further development was halted until prototype completion. If a limit switch is activated, an interrupt routine drives the H-bridge low and throws an error; putting the H-bridge on hold is redundant, as the wiring, described in subchapter 3.2, already cuts the power to the motor; as a result, the system has triple redundancy for emergency stop: software defined limits, external interrupt routine and hardware-defined limits, so even in case of end-user interference with the safety checks, it is reasonable to expect that at least one remains active.

## **4. Conclusions**

This paper presented the design stages of a hybrid 2-DOF lower limb exerciser; although the work done so far is enough to grant the manufacture of a first prototype, several issues were identified and are taken into account for a future iteration. First of all, it is necessary to make sure that the exerciser is capable of serving a broader demographic; even though the selected motors have a 8-fold power margin, there was no rigorous calculation of the needed torque in order to cover at least the 95th percentile for height and mass of the population. A useful improvement would be the addition of strain gauges; not only would the operational safety increase (if an anomalous strain is detected, the exerciser stops and avoid potential injury), but it would also enable active and passive mode usage. Therefore, a patient might continue to use the exerciser for different stages of their rehabilitation; in the beginning, when the musculature is still weak, the system might work in a passive mode to maintain articular mobility; in the later stages, when the musculature begin to strengthen, the exerciser might switch to an active mode, opposing the movement with a certain force controlled by the strain gauges.

Another design requirement for a future iteration is the simplification of the actuating system; one of the DOF is directly connected to the motor, which makes the actuation very robust. The second DOF is connected with a quite complex transmission which is prone to failure. There are already several design solutions being investigated, but not fully explored at this time. Modern equipment tends to have implemented diverse communication protocols that use the radio spectrum; in this regard, a future development will be the addition of a Bluetooth module that will enable communication with

a smartphone app. Another idea worth investigating is implementing Wi-Fi functionality, but this direction must be carefully approached, as connecting a medical device to a computer network might expose the patient to malicious actors over the internet. Another planned improvement is related to multiple exercise selection: in preparation for the prototype, the designed code is capable of reading only one file; a file management system has to be implemented, which will allow multiple exercise files to be loaded on the SD card and chosen by the physical therapist or patient, presumably with a Bluetooth-connected smartphone. As soon as full activity in the Biomechatronics Laboratory is allowed (currently reduced by measures taken to stop the spread of SARS-CoV2), a prototype will be build using the additive manufacturing technologies available; this prototype will be further used for preliminary testing, and, if found satisfactory, pre-clinical testing using healthy volunteers.

**Author Contributions:** Conceptualization, D.L. and A.I.-A.-D.; methodology, A.I.-A.-D.; software, L.I.V.; validation, A.I.-A.-D.; formal analysis, A.I.-A.-D.; investigation, L.I.V.; resources, L.I.V.; data curation, A.I.-A.-D.; writing—original draft preparation, D.L.; writing—review and editing, D.L.; visualization, A.I.-A.-D.; supervision, A.I.-A.-D.; project administration, A.I.-A.-D. All authors have read and agreed to the published version of the manuscript.

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

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

## **References**


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## *Proceedings* **A New Light Aircraft and Its Design Method** †

## **Marius-Ion Ghit,escu 1,\*, Marilena Ghit,escu <sup>1</sup> and Arina Modrea 2,\***


Published: 22 January 2021

**Abstract:** The paper presents some aspects related to a new light aircraft that has as fields of use sports and leisure aviation. It also has a maximum capacity of two seats and a certain aerodynamic shape and which has on the wings mounted curved flaps for the flight board without hinges, as well as for gliding the plane in critical flight conditions or when it is necessary to save fuel. The paper presents and optimal design method of this new light aircraft.

**Keywords:** light aircraft; design method; optimal; symmetric geometry

## **1. Introduction**

The activity of designing a product part uses knowledge acquired in the fields of mathematics, physics, strength of materials, technical drawing, study of metals, materials technology, tolerances and dimensional control, technology of machine construction.

Aircraft design is an information intensive engineering process full of evaluation and decision-making. Conceptual design phase, compared with the entire design process, consumes relatively less time and costs; however, many tasks should be carried out, and a lot of important decisions will have to be made during this period. It is estimated that as much as 80% of the life cycle costs of an aircraft is decided in the conceptual design and preliminary design phase [1–3].

The wing loading is the weight of the aircraft divided by the area of the reference (not exposed) wing. As with the thrust-to-weight ratio, the term "wing loading" normally refers to the takeoff wing loading but can also refer to combat and other flight conditions. Wing loading affects stall speed, climb rate, takeoff and landing distances and turn performance. The wing loading determines the design lift coefficient, and impacts drag through its effect upon wetted area and wing span. Wing loading has a strong effect upon sized aircraft takeoff gross weight. If the wing loading is reduced, the wing is larger. This may improve performance, but the additional drag and empty weight due to the larger wing will increase takeoff gross weight to perform the mission [4].

Aircraft sizing is the process of determining the takeoff gross weight and fuel weight required for an aircraft concept to perform its design mission.

It is known in the literature the light aircraft Extra 300 LT at which the force load of the direction reaches 90 kg [5]. The Extra 300 LT is a one- or two-seater acrobat aircraft produced by German manufacturer Extra Aircraft (Extra Flugzeugbau GmbH, today Extra Flugzeugproduktions- und Vertriebs-GmbH).

It is known the Zlin 142 light aircraft at which the load with forces reaches 200–250 N [6]. Zlin Z 142 is a single-engine aircraft with two seats for tourism and produced by Czechoslovak manufacturer Moravan Otrokovice (now ZLIN Aircraft Otrokovice, Czech Republic).

The new light aircraft has as its areas of use sports and recreational aviation with a maximum capacity of two seats [7].

The new light aircraft has a certain aerodynamic shape, symmetry geometry and good stability being made up of middle wings of rectangular shape and having in part an asymmetrical profile so that the profile rope forms an angle of incidence ϕ*incidence* = 11◦ with the direction of advance and a setting angle ϕ*calaj* = 0◦, from a front fuselage with a certain aerodynamic shape, a central fuselage with a certain aerodynamic shape and having 2 parts of different shapes in the cabin area, a rear fuselage with a certain aerodynamic shape, propeller helmet, ailerons, flaps, cabin, depth, drift, direction, stabilizer with profiled shapes [8–10].

## **2. A New Light Aircraft and Optimal Design Method**

The technical problem of a new light aircraft is the improvement of the dynamic behavior of the light aircraft through the control mechanisms of the flaps and the constructive form of the aircraft, in the conditions of low manufacturing costs and in a favorable time for the aircraft, increasing the surface of the flaps, increasing the wingspan to allow the aircraft to operate in critical flight conditions or when fuel economy is required, enabling the aircraft to glide in these situations.

The design of the aircraft took into account the fact that the components of the aircraft must be simple to manufacture and assemble and accessible for repair.

When establishing the aerodynamic shape and the constructive dimensions of the light aircraft, the optimal design of the light aircraft was taken into account, as were the parameters that influence the aerodynamic shape of the fuselage and wing (Figures 1–5), as well as the flap and aileron installations and mechanisms mounted in these areas.

**Figure 1.** A new light aircraft. 1—the median wing of rectangular shape and having in part an asymmetrical profile so that the chord of the profile forms an angle of incidence with the direction of advance and an angle of choke of a certain length *L*, 2—the central plane of the fuselage, 3—the helmet of the propeller, 4—front fuselage (bonnets), 5—aileron, 6—curved flaps or single flaps (one on each wing) located on the trailing edge without hinges (without axes of rotation on the wings), 7—the cab, 8—the depth (the moving part of the horizontal tail), 9—the drift (the fixed part of the vertical tail), 10—the direction (the moving part of the vertical plumage), 11—rear fuselage, 12—stabilizer (fixed part of the horizontal tail), 13—central fuselage (2nd part).

**Figure 2.** Lateral view of a new light aircraft.

**Figure 3.** The frontal view of light aircraft.

**Figure 4.** The first part of fuselage.

**Figure 5.** The central fuselage—Part 1.

The constructive solution of the new light aircraft consists of original components such as shape and dimensions to improve the aerodynamics of the aircraft and its stability, as follows: median wings, *L*-shaped, rectangular and having in part an asymmetrical profile so that the rope profile forms an angle with the forward direction, the central plane of the fuselage (Part 1 of the central fuselage), the propeller helmet, the front fuselage (hoods), ailerons and curves for the flight dashboard without

hinges (one on each wing), the cabin housing the crew, the depth, the drift, the direction, the rear fuselage, the stabilizer and the second part of the central fuselage.

The advantages of the light aircraft are the following:

(a) The light aircraft has a simple and fast response structure, is safe and reliable and has good flight control and lifting performance and good stability.

(b) The aerodynamic shape of the airplane and the constructive shape of the flywheel control mechanism imply an increased service life.

(c) In order to increase the lift capacity of the aircraft, during take-off and landing, as well as during the flight, two curved flaps for the flight board without hinge (without axes of rotation with respect to the wings) were mounted on the wings, one on each wing.

(d) By increasing the length of the wings, an increased load-bearing surface was obtained, increasing the wingspan *L* of the wings to a value greater than (1.1 ... 1.3) times the length of the fuselage *Lf*, which led to an increase in the surface of the flaps, which allows the aircraft be able to glide in critical flight situations when the engine is no longer running or when needed for fuel economy, which allows the aircraft to easily behave like a glider.

Figure 1 shows in axonometric view the constructive solution of a new light aircraft, which consists of original components as a shape and dimensions to improve the aerodynamics of the aircraft and its stability, as follows: 1—represents the median wing of rectangular shape and having in part an asymmetrical profile so that the chord of the profile forms an angle of incidence with the direction of advance and an angle of choke of a certain length L (2 pcs.), 2—the central plane of the fuselage, 3—the helmet of the propeller, 4—front fuselage (bonnets), 5—aileron (2 pcs., one on each wing), 6—curved flaps or single flaps (one on each wing) located on the trailing edge without hinges (without axes of rotation on the wings), 7—the cab, 8—the depth (the moving part of the horizontal tail), 9—the drift (the fixed part of the vertical tail), 10—the direction (the moving part of the vertical plumage), 11—rear fuselage, 12—stabilizer (fixed part of the horizontal tail), 13—central fuselage (2nd part) [7].

The aerodynamic shape and construction dimensions of this aircraft have been established by combining various geometric shapes for its components in order to obtain a good aerodynamic shape for the class of light aircraft and to fulfill the function of gliding when needed when fuel economy is needed or in critical flight conditions when the engine is no longer running.

The aerodynamic shape and constructive dimensions of the light aircraft shown in Figures 1–3 make this aircraft also fall into the category of glider, which means that the aircraft can glide as needed if the engine is no longer running or when the engine is stopped for fuel economy.

Figure 2 shows a side view of the light aircraft in which the important components and dimensions established in the design of the aircraft can be observed.

The aerodynamic shape of the light aircraft depends on the aerodynamics of the body systems of which the aircraft is composed. The fuselage being the supporting organ of the plane's transport load, its design starts from the interior partitioning necessary for the plane's mission.

The fuselage of a light aircraft consists of 3 large assemblies, namely, assembly 1 called the front fuselage 4 (front of the aircraft) in length, assembly 2 called the central fuselage which has 2 parts 1 and 2 (positions 2 and 13 lengths), and the last assembly being the rear fuselage 11 (from the tail of the plane) long.

The shape of the fuselage on light aircraft without special demands of an aerodynamic nature is imposed by technological considerations, manufacturing costs and useful volume.

The useful volume is the parameter that gives the available space inside where we can place the crew, luggage, equipment and fuel.

The payload depends on the carrying capacity of an aircraft which decreases with the reduction of the total length of the fuselage and the area of the maximum cross part.

A maximum useful aircraft volume means a lower than optimal aerodynamic shape.

The fuselage of the aircraft is located in a stream of air and it produces lift (very low) but especially forward resistance: Lateral aerodynamic forces and aerodynamic moments act on it; its construction takes over all the demands of the other organs and elements of the aircraft.

In addition, in the fuselage are arranged spaces for crew, propulsion system, fuel tank, equipment, etc., which implies the existence of a well-defined volume. For the fuselage, an optimal solution must be found both from an aerodynamic and constructive point of view: with a front surface as small as possible to "close" a large volume, but at the same time, the shape of the body volume obtained, to be as aerodynamic as possible.

The front fuselage of a light aircraft, Figures 2 and 4, has an aerodynamic profiled shape, being made up at the bottom of a surface arranged under a circular arc on a length *La*, the straight side surfaces on the length *La* = (1.2 ... 1.5)\**Df*, and the part of above is a flat surface that is inclined at a certain angle δ = 20◦ ... 50◦ .

The maximum equivalent part *Df* = H [mm] for the center fuselage shall be determined according to the dimensions of the cab and of the installations which are contained in the fuselage.

For light aircraft with 2 adjacent seats, the area of the maximum rear fuselage part is recommended as *Sf* = 1.5 ... 1.7 m2. Determining the total length of the fuselage with the relation: Lf = (6 ... 10)\**Df*, where *Lf*/*Df* = *lf* = 6 ... 10 represents the elongation of the fuselage.

At subsonic flight speeds, the pressure resistance in a laminar flow is relatively low compared to the frictional resistance, and there is no question of reducing it. As the forward resistance is mostly produced by the frictional resistance, it is recommended to use short (shorter) fuselages to reduce it.

The central fuselage has two aerodynamic parts (Figures 1, 2 and 5).

Part 1 of the central fuselage of a light aircraft has at the bottom a surface arranged under an arc of a circle on a length *L*<sup>1</sup> = *L*<sup>2</sup> = (1.7 ... 2.0)\**Df*, straight side surfaces; the top is straight, a front surface facing the cab inclined at a certain angle δ*windscreen* = 40 ... 55◦, having in longitudinal part a profiled shape with dimensions *h* = 0.625*\*Df*, *L*1, *Df*, *H* = *Df* = (1.5 ... 1.7)\**h* and an inclined front surface which is the windscreen inclined at a certain angle δ*windscreen* = 40 ... 55◦ for optimum visibility, Figure 5.

Part 2 of the central fuselage of a light aircraft (Figures 2 and 6) has a profiled aerodynamic shape having at the bottom a surface arranged under an arc of a circle on a length *L*<sup>2</sup> = *L*<sup>1</sup> and inclined at an angle δ<sup>1</sup> = (10◦ ... 25◦), the straight side surfaces, and the top is a flat and inclined surface at a certain angle δ<sup>1</sup> = (10◦ ... 25◦), having in longitudinal part a frustoconical shape with large base *H* = *Df*, length and angle of inclination of the side edges δ<sup>1</sup> = (10◦ ... 25◦).

**Figure 6.** The central fuselage—Part 2.

The shape of the rear fuselage is shown in Figures 1 and 7. The rear fuselage of a light aircraft has a profiled aerodynamic shape, being formed at the bottom of a surface arranged under an arc of a circle on a certain length *Lp*<sup>1</sup> = 0.7\**Lp*; the left-right side surfaces are straight on a certain length *Lp*<sup>1</sup> = 0.7*\*Lp*, and the surfaces from the tail of the plane are inclined at a certain angle θ*<sup>p</sup>* = 20 ... 50◦ on a length *Lp* − *Lp*<sup>1</sup> = 0.3*\*Lp*, where *Lp* = (1.2 ... 2.5)\**Df*.

**Figure 7.** The rear fuselage.

The middle wing of a light aircraft (Figures 1–3) has a profiled aerodynamic shape, the wing having a rectangular shape and an asymmetrical profile in part so that the profile rope forms an angle of incidence ϕ*incidence* = 11◦ with the direction of advance and a right angle. ϕ*chocking* = 0◦, and the wingspan *L* of the wing is greater than (1.1 ... 1.3) times the length of the fuselage *Lf* = (6 ... 10)\**Df*, (*Df* = *H* [mm]—the maximum equivalent part for the central fuselage, for a non-circular profile) to allow the aircraft to behave like a glider due to the length of the wings and the aerodynamic shape, to glide when needed for fuel economy or in critical flight situations when the engine is no longer running.

The middle wing is advantageous in terms of interaction with the fuselage.

Figure 3 shows a front view of the light aircraft and the wingspan *L* of the wings.

When designing the fuselage of the aircraft, the operating conditions necessary for the fuselage were taken into account: maximum payload, access to all installations mounted in the fuselage, heating, ventilation, tightness, good visibility for the crew. The strength and rigidity of an aircraft are maximum at a minimum weight of the resistance structure.

The design of the aircraft took into account the fact that the components of the aircraft must be simple to manufacture and assemble and accessible for repair.

Increasing the length of the wings also increases the length of the flaps, which leads to increased lift during takeoff and landing of the aircraft slightly.

At subsonic flight speeds, a great influence on the aerodynamic characteristics has also the attack board of the wing profile, reason for which its sharp shape is avoided because it does not allow obtaining large lifting forces.

When the plane flies at relatively low speeds, the evolutions are made at high angles of incidence. The detachment of the boundary layer that begins with the increase of the angles of incidence is manifested with greater intensity in the area where the wing joins the fuselage. This detachment results in an increase in the forward resistance, a decrease in lift and a displacement of the center of pressure.

Upon landing, the pilot reduces engine traction and automatically reduces the lift. Volleyballs driven at negative downward angles ensure an increase in lift at this critical time, behaving like an aerodynamic brake.

At take-off, the traction of the engine increases successively, and the flaps as hypersuspension devices ensure an increase of the load-bearing force and the reduction of the take-off distance.

*Proceedings* **2020**, *63*, 66

The optimal design method of the light aircraft is to establish the calculation steps that define the parameters of the fuselage and the wing and the aerodynamic shape of this aircraft depending on the maximum equivalent part Df in the cabin area where the crew sits, the value of the magnitude *L* = (1.1 ... 1.3)\**Lf*, of the installations that are mounted in these areas.

Figure 8 shows the logic diagram underlying the optimal design of the aerodynamic shape of a light aircraft with the steps to be followed.


$$(L\_a + L\_1) \% L\_f = 0.2 \dots \text{ 0.3}$$

where *La* [mm] represents the length of the front fuselage, *L*<sup>1</sup> [mm]—the length of Part 1 of the central fuselage (cabin area), *L <sup>f</sup>* [mm]—the total length of the fuselage.

4. The determination of the elongation of the front fuselage is calculated with the relation:

$$L\_a/D\_f = 1.2 \dots \dots \text{ 1.5 or } L\_a = (1.2 \dots \dots \text{ 1.5})^\* D\_f \text{ [mm]}.$$


$$\begin{array}{rcl} L\_1 = L\_2 = (1.7 \dots \text{2.0}) \ast D\_f \text{ [mm]}, \delta\_1 = 10^\circ \dots \text{ 25}^\circ, \\ L\_c = L\_1 + L\_2 = 2 \ast L\_1 = 2 \ast L\_2 = (3.4 \dots \text{4.0}) \ast D\_f \text{ [mm]}. \end{array}$$

where *L*<sup>1</sup> [mm]—length of Part 1 of the central fuselage (in the cab area), *L*<sup>2</sup> [mm]—the length of Part 2 of the central fuselage, *Lc*—the total length of the central fuselage, and δ1—the angle of inclination of the side edges.

7. The establishment of the lateral surface of the fuselage is approximated with the relation:

$$S\_{\rm lat} = K \pi D\_f L\_f = \left[ 0.734 + 14.5 \times 10^{-3} \times (6 \dots 10) \right] \pi D\_f L\_{f'} \left[ \text{mm}^2 \right]$$

where *<sup>K</sup>* <sup>=</sup> 0.734 + 14.5 <sup>×</sup> <sup>10</sup>−<sup>3</sup> <sup>×</sup> (6...10).


$$h = 0.625 \ast D\_f.$$

12. The determination of the width *l* [mm] of the cabin is determined with the following relation:

$$l = 1.0625 \ast D\_f.$$

13. The determination of the height *H* [mm] is determined by the following relation:

$$H = D\_f = (1.5 \dots 1.7) \ast h\_r$$

*Df* = 1.6\**h* was adopted.

14. The determination of the height *Ha* [mm] of the direction is determined by the following relation:

$$H\_a = (1.2\ldots1.3) \bullet D\_f.$$

*Ha* = 1.235\**Df* was adopted.


The optimal method of designing the light aircraft is to go through the following steps:

When the aircraft is operating lightly, the two flaps on the wings bend (rotate downwards) symmetrically, only at negative angles.

During the flight of the aircraft, the two identical ailerons on the wings brace anti-symmetrically to each other at positive and negative angles and generate the roll motion.

In the current stage of industrial development in conditions of high competition in the aero industry market, each manufacturer must develop its own strategy.

It seeks to reduce as much as possible the time interval between the conception (design) of an installation and its execution.

For this purpose, the use of the computer in all stages of design and production is a basic requirement. Thus, it is necessary:


Aircraft must comply with special design and execution conditions. These apply to all subassemblies and components.

Computer modeling and virtual prototyping are valuable tools for creation.

The materials used for its execution also have an influence on the aerodynamics of the light aircraft and its minimum weight. The main components of the light aircraft (for example, fuselage, wings, tailings, throttle controls, ailerons) can be made of various materials (e.g., duralumin or composite materials) so as to obtain good aerodynamics and a minimum weight of plane.

By using composite materials, the weight of the aircraft is considerably reduced, the aerodynamics is improved, and its mechanical strength and reliability are increased.

**Figure 8.** The logic diagram of optimal design method of light aircraft.

#### **3. Conclusions**

The process of aircraft conceptual design includes numerous statistical estimations, analytical predictions and numerical optimizations. However, the product of aircraft design is a drawing. While the analytical tasks are vitally important, the designer must remember that these tasks serve only to influence the drawing, for it is the drawing alone that ultimately will be used to fabricate the aircraft.

All of the analysis efforts to date were performed to guide the designer in the layout of the initial drawing. Once that is completed, a detailed analysis can be conducted to resize the aircraft and determine its actual performance.

This detailed analysis is time-consuming and costly, so it is essential that the initial drawing be credible. Otherwise, substantial effort will be wasted upon analyzing an unrealistic aircraft.

The design layout process generally begins with a number of conceptual sketches.

A good sketch will show the overall aerodynamic concept and indicate the locations of the major internal components. Once the design has been analyzed, optimized, and redrawn for a number of iterations of the conceptual design process, a more detailed drawing can be prepared.

The crew station will affect the conceptual design primarily in the vision requirements.

Requirements for unobstructed outside vision for the pilot can determine both the location of the cockpit and the fuselage shape in the vicinity of the cockpit. The pilot must be able to see the runway while on final approach, so the nose of the aircraft must slope away from the pilot's eye at some specified angle. While this may produce greater drag than a more streamlined nose, the need for safety overrides drag considerations. Similarly, the need for over-side vision may prevent locating the cockpit directly above the wing.

The vision angle looking upward is also important. Light Aircraft should have unobstructed vision forwards and upwards to at least 20 deg above the horizon.

By increasing the length of the wings, an increased load-bearing surface was obtained, increasing the wingspan L of the wings to a value greater than (1.1 ... 1.3) times the length of the fuselage *Lf*, which led to an increase in the surface of the flaps, which allows the aircraft be able to glide in critical flight situations when the engine is no longer running or when needed for fuel economy, which allows the aircraft to easily behave like a glider.

Computer modeling and virtual prototyping are valuable tools for creation.

By applying a virtual prototyping algorithm, we can shorten the distance between the creation and execution of the physical prototype. By increasing the length of the wing and the wingspan, the surface of the flaps is obtained. By increasing the surface of the shutters, the load is increased. By increasing the load and by increasing the steering angles, the take-off and landing of the aircraft is done in a shorter time and over a shorter distance.

#### **4. Patents**

The content of this paper is the subject of a patent application entitled "*Light aircraft and flap control mechanism*".

**Author Contributions:** Conceptualization, M.-I.G.; methodology, M.-I.G., M.G. and A.M.; software, M.-I.G. and M.G.; validation, M.-I.G.; formal analysis, M.-I.G., M.G.; investigation, M.-I.G.; resources, M.-I.G.; data curation, M.-I.G.; writing—original draft preparation, M.G.; writing—review and editing, M.G. and M.-I.G.; visualization, M.G.; supervision, M.-I.G. and A.M. All authors have read and agreed to the published version of the manuscript.

## **References**


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