Optimal Design of a Parallel Manipulator for Aliquoting of Biomaterials Considering Workspace and Singularity Zones

Round 1

Reviewer 1 Report

The paper describes a new proposal for biological samples manipulation consisting of a robotic system that comprises a serial robot and a Deli robot. The paper follows describing the deli robot kinematics analysis and optimization for the Delta robot.

The article seems interesting but lacks on delivering information on various aspects.

The application of the proposed solution is discussed in section 2 where a brief introduction of equivalent solutions, then, it is described which requirements the solution must fulfill but later it is not explained how these requirements are fulfilled. For example, page 5 is dedicated to describe the dispensing head and the fixation of the pipette that seems to be a commercial solution and not a new design. Either this novelty is not well stablished (there is no comparison to other available solutions) or it will be more interesting to explain other aspects of the solution, as the advantages of using a parallel manipulator against the serial mechanism solutions present in the alternatives.  The only justification for the use of the parallel robot is the speed (some biological samples cannot be handled at high speeds so the advantage is not clear, as it is clearly stated in requirement 10) and the accuracy of the movement (again, the needed accuracy is not specified), so the advantages of the solution must be more clearly explained.

Later the paper describes the kinematics of the deli manipulator. This part is quite confusing. It is stated that the manipulator is based on the delta robot with an additional degree of freedom. I must suppose that this additional degree of freedom just actuates the end effector as is not further mentioned during the paper. This type of robot is widely studied, and it is no clear the novelty of the analysis either in the kinematics study, workspace analysis or interference analysis. The authors must either clearly explain the novelty of the proposed solution against other studies of the same parallel manipulator or reduce the length of this sections. More importantly, it seems that the kinematic chain for the actuation of the end effector (two or three bars connected by spherical joints as seen in Figure 6???) is not considered for the interference study, why??

In these sections, it is also interesting that the study or optimization is made considering the whole volume of the manipulator, but the application is clearly only going to need a very small portion of it. Has this fact been considered during the optimization? If not why?

In summary, if the paper is proposing a new robotic solution for biological sample manipulation, the solution is poorly explained and there are a lot of requirements that are not correctly explained to evaluate if they are fulfilled. On the other hand, if the paper is proposing a new optimization procedure, the bibliography must be extended comparing other optimization works applied to the same manipulator.

 

Additional comments: There are some minor grammar and typo mistakes throughout the paper, for example: line 45, the accuracy of the taken into account characteristics; lines 284 and 285 sentence is confusing. Line 335 a space is missing.

Description of the interference algorithm should be improved providing and image with the mentioned vectors and magnitudes.

Author Response

Thanks a lot to the reviewer for the comments!

Requirements in section 2, which do not affect the choice of geometric parameters of the DeLi manipulator, are excluded. Added all the requirements that are taken into account when calculating the manipulator's required range of vertical movements. The requirements are taken into account when describing the additional optimization process, which is presented at the end of the article.

The authors have designed an excavating head, so it can be attributed to both a new technical solution and a commercial solution if it will be used in a serial sample.

The requirements state that the movement of tubes with fractionated whole blood samples must be carried out at a limited speed. However, the blood is divided into fractions only at the stage of its movement by the Uni manipulator. The DeLi manipulator dispenses only one fraction of blood. Therefore, the movement speed for the DeLi manipulator is not limited. At the same time, in addition to high speed, the DeLi manipulator has a number of advantages in comparison with sequential mechanisms, including accuracy, rigidity, maneuverability within the workspace, less weight of links, no additional guides in the workspace, ease of installation of the vision system and a host of other advantages. which allow it to be used for different applications. The workspace of ​​the DeLi manipulator is freer, there are no bulky parts. Less mass allows for less inertia. A description of these benefits has been added to the article.

During the initial synthesis of the manipulator structure, an additional kinematic chain was provided to provide the fourth degree of freedom required for the rotation of the end-effector. In the future, it was decided to replace the additional kinematic chain with an electric drive installed inside the excavating head, due to the low values ​​of the required torque. In this regard, the additional kinematic circuit has been removed from the circuit in Figure 6.

The analysis of the workspace is based on the well-known methods of interval analysis, however, using the algorithm for determining the interference of links developed by the authors. At the same time, in the existing works on the analysis of the workspace of the Delta mechanism, little attention is paid to the analysis of the influence of singularity zones and interference of the links on the quantitative change in the volume of the workspace, taking into account various solutions of the inverse problem of kinematics. In addition, the novelty of the work in general is associated with the development of a new system consisting of several robots, as well as the design of the system taking into account the specific requirements of aliquoting and additional modules such as the excavating head.

Additional kinematic chain is not considered in the investigaton of interference, since it is excluded from the structure of the manipulator.

The comment of the reviewer about accounting not for the entire volume of the workspace, but only for its part required to complete the aliquot task, was taken into account. Additional optimization has been added at the end of the article. The additional optimization criterion takes into account the diameter of the cylindrical area that can fit into the workspace. The height of the cylindrical area is selected based on the requirements for the required range of vertical movements of the DeLi manipulator.

The review has added an analysis of other works on the optimization of Delta mechanics, substantiating the relevance of the investigation.

Errors and misprints corrected. There is a reference аfter the algorithm to the article of the authors, which describes in detail the process of determining the interference of links.

Reviewer 2 Report

The paper is technically good. The motivations and objectives are well clarified. The presentation may be improved aiming better readability.

 

Author Response

Thank you very much to the reviewer for the appreciation of our work!

Reviewer 3 Report

The manuscript considers a robotic system for medicine, specifically to collect and analyze biological samples. While overall correct, the work presented appears of limited scientific novelty. I am therefore recommending rejection; while some concepts presented may have some merit, I believe this study would require significant expansion to be of sufficient interest. My notes are reported below.
1)    The connection of the design proposed with medical robotics appears tenuous at best. Many details are provided on laboratory practice for analysis of biological samples, together with bibliographic references, yet the actual content is on the workspace analysis of a robot that could be applied to many other fields. The concept of "aliquoting", which is referenced several times across the paper, is never actually explained, assuming that the reader is familiar with biological laboratory practice (yet the Special Issue for which it has been sent is on robotics). The connection of this work with the COVID19 pandemic appears even less relevant. The need for robotization in this field is not mentioned in the cited reference [3] (see page 1). The details on pipetting devices on p. 5 could be significantly shortened. In brief, the goal of developing "an intelligent robotic system that considers the variation in the volume of the initial samples and the presence of different phases of liquid in them" (p. 2) does not appear to have been reached.
2)    No experimental results are provided and the design of the Delta parallel robot is only sketched, by finding its dimensions; no CAD model is presented. Notice that this is a classical architecture, that has been studied since the '80s: the novelty thus seems limited.
3)    The main topic is the workspace analysis of a Delta robot, considering both singularities and interference between links. The literature on workspace and singularity analysis for parallel robots is too vast to be described here; reference works such as "Robot analysis" (L.-W. Tsai, Wiley, 1999), "Parallel robots" (J.-P. Merlet, Springer, 2005) or "Singularities of robot mechanisms" (O. Bohigas et al., Springer, 2017) contain hundreds of references on the matter. The manuscript however barely mentions previous works on these topics; out of 32 references, 14 are from at least one of the authors, but their relevance appears questionable (see Refs. [11-12]: how are cable robots relevant here?). A full bibliographic review ought to be carried out, considering seminal previous works on efficient algorithms for workspace analysis of parallel robots, to prove the novelty of the approach presented here.
4)    After workspace analysis, the kinematic parameters of the robot are optimized. This is achieved, from what I understand (the description on p. 17-18 appears vague), through trial-and-error. Thus, it is unlikely that the globally optimal architecture has been found; compare this approach with the state of the art on multi-variable, multi-objective optimization algorithms available in the literature. Moreover, the optimization only appears to consider the workspace volume, while a robust design must take into account several other parameters (such as kinematic and dynamic performance, error transmission, stiffness maximization and so on): optimizing exclusively for workspace volume easily leads to designs that are in fact poor when considering other desirable characteristics.
5)     The robot model seems incomplete. The variables a, c, d and so on, used from p. 6 onward, are not defined in the text; also, the "DeLi" robot is not defined (is it a novel architecture? Has it been presented elsewhere?). A kinematic chain with two spherical joints is shown (Figs. 6-13) but its effect on intra-link interference is not considered (Sec. 5). I also do not understand how a singularity surface (which is two-dimensional) can "reduce" a workspace (which is a 3D volume); note that there are algorithms that allow a robot to pass through a singularity by taking advantage of its own dynamics. The algorithm presented in Sec. 3 to approximate the workspace appears very similar to interval analysis; see "Introduction to interval analysis" (R. E. Moore et al., SIAM, 2009).

Author Response

1. Additional optimization was added at the end of the article. The additional optimization criterion considers the diameter of the cylindrical area that can fit into the workspace. The height of the cylindrical area is selected based on the requirements for the required range of vertical movements of the DeLi manipulator. Aliquot word is explained. The development of a system for aliquoting (biosample analysis) is very relevant in connection with COVID19 from a practical point of view. The number of biosamples investigations has increased recently.
Robotization makes it possible to reduce the duration of the investigation of biological samples, minimize the number of manual labor operations, increase the accuracy of the taken into account characteristics of the samples, and reduce the time of their storage at room temperature. Improving the quality of biosamples is the basis for ensuring the representativeness and reproducibility of research results. This eliminates the time-consuming operation to separate the blood clot from the serum by the operator, which
increases the use of consumables, increases the risk of errors and contamination of laboratory equipment surfaces.
In the proposed robotic system, the dosing device is installed on the DeLi manipulator. In this regard, the description of its design is appropriate in this article.

2. Experimental verification of the results obtained will be carried out in the framework of future investigations. The architecture of the Delta robot has been known for a long time, but the novelty of the technical solution presented in this article lies in the fact that an excavating head supplements this mechanism with an electromechanical drive, which was designed by the authors and taking this link into account affects the workspace.

3. The list of references has been edited. In the existing works on the analysis of the workspace of the Delta mechanism, little attention is paid to the analysis of the influence of singularity zones and interference of the links on the quantitative change in the volume of the workspace, taking into account various solutions of the inverse problem of kinematics. In addition, the novelty of the work in general is associated with the development of a new system consisting of several robots, as well as the design of the system taking into account the specific requirements of aliquoting and additional modules such as the excavating head.

4. Additional optimization was performed taking into account the peculiarities of the aliquot problem. The authors agree with the remark of the reviewer about the need to take into account the dynamic characteristics.
However, in this work, the task was to investigate the influence of singularity zones and interference of links, which significantly reduce the workspace, including in accordance with the technological process of aliquoting, which is important to consider when designing such structures.

5. Added mention of variables a, c, d in the text. The DeLi robot is based on the existing Delta-type mechanism, but with a link with an electromechanical drive for setting the pipette for digging out biomaterial.
Added references to sources in which the Delta-type mechanism was previously investigated.
During the initial synthesis of the manipulator structure, an additional kinematic chain was provided to provide the fourth degree of freedom required to rotate the end-effector. In the future, it was decided to replace the additional kinematic chain with an electric drive installed inside the excavating head, due to the low values of the required torque. In this regard, the additional kinematic circuit has been removed from the circuit in Figure 6. The algorithms suggested by the reviewer that allow a robot to pass through a singularity can be applied to serial robots or to some robots based on 5-bars architecture where it is possible to use the robot inertia to overcome the singularities. Delta robots can be used only in one of the two configurations. The workspace analysis is based on the well-known methods of interval analysis, however, using the algorithm for determining the interference of links developed by the authors.

Round 2

Reviewer 1 Report

The authors have improved the quality of the work, but the novelty or results still seems hard to evaluate.

As stated by the authors, “the task arises of creating an intelligent robotic system that considers the variation in the volume of the initial samples and the presence of different phases of liquid in them”. How does the proposed solution improve or solve this problem? This fact, has not been addressed in the paper, and as stated before, the main contribution of the work is unclear.

This new description (lines 131-138) seems to add more confusion. I can not see the advantages of the proposed solution against other solutions presented in the introduction, for example the OT-2 from opentrons, which seems less cumbersome, meet the specified requirements and seems to be easier to implement any visual inspection hardware since there are no limbs present inside the system. It does not implement an additional serial robot, but again, this serial robot is mentioned in the description, but never mentioned or studied again.

The authors state that they have designed a new excavating head. Do they refer to the dispensing head, the digging head? Please, use the same name for the same elements since its very confusing for the reader. Also, if this is a mayor contribution of this work, it seems that the explanation is quite short and lacks any conclusions regarding the requirements that it fulfills. Additionally, no state of the art is presented regarding this element, which should be included if this is a mayor contribution of the work.

As the authors have stated, this design is just a Delta robot with a different tool. Considering this, it is necessary to call it Deli?

The additional optimization seems to be introduced in a hasty way. A cad model of the final solution and its position in the robotic system is necessary to evaluate if the solution is applicable (obtained lengths seem a bit large comparing to other solutions explained in the introduction).

Author Response

The authors have improved the quality of the work, but the novelty or results still seems hard to evaluate.

 

As stated by the authors, “the task arises of creating an intelligent robotic system that considers the variation in the volume of the initial samples and the presence of different phases of liquid in them”. How does the proposed solution improve or solve this problem? This fact, has not been addressed in the paper, and as stated before, the main contribution of the work is unclear.

 

The authors agree with the reviewer's comments regarding the issue of different phases of the liquid. This issue has not been considered in detail, in connection with this information about this we have removed from the article. More important was the issue of suppression of workspaces, taking into account the implementation of the technological process of aliquoting. Additional investigations and modeling were carried out, this material was added to the article in section 7.

 

This new description (lines 131-138) seems to add more confusion. I can not see the advantages of the proposed solution against other solutions presented in the introduction, for example the OT-2 from opentrons, which seems less cumbersome, meet the specified requirements and seems to be easier to implement any visual inspection hardware since there are no limbs present inside the system. It does not implement an additional serial robot, but again, this serial robot is mentioned in the description, but never mentioned or studied again.

 

Description has been changed. The authors have choosen a delta parallel robot topology due to the fact that it has a better performance in terms of dynamics and accuracy as compared with serial robots (including OT-2 from opentron). Furthermore, delta architectures are better suited for moving along curvilinear trajectories that may arise in the proposed specific application due to different heights of test tubes and racks. This makes the delta architecture better suited also in comparison with portal architecture. The implementation of an additional serial robot is explained and supplemented. The relative position of the robots was determined, and the intersection of the DeLi and Uni workspaces was built. The volume of the area of intersection of the workspaces of the robots is sufficient to accommodate a medical rack with 96 test tubes with a biological fluid divided into fractions.

 

The authors state that they have designed a new excavating head. Do they refer to the dispensing head, the digging head? Please, use the same name for the same elements since its very confusing for the reader. Also, if this is a mayor contribution of this work, it seems that the explanation is quite short and lacks any conclusions regarding the requirements that it fulfills. Additionally, no state of the art is presented regarding this element, which should be included if this is a mayor contribution of the work.

 

The authors have corrected the remark about the different definitions used. Now one definition is used everywhere - "dispensing head". However, it is not the main contribution to the work. The main purpose of this work is to determine the analysis of the workspace of the delta robot, taking into account singularity zones and interferences of links for various configurations and the optimization of geometric parameters for two cases. The volume of the workspace is the criterion for the first optimization. A criterion that takes into account the compactness of the design and the maximization of the workspace, taking into account the requirements of the process of aliquoting along the height of the workspace, is used for the second optimization.

 

As the authors have stated, this design is just a Delta robot with a different tool. Considering this, it is necessary to call it Deli?

The authors agree with the remark about the name of the parallel robot. In this investigation, a standard delta robot with a dispensing head tool is used, but the designation DeLi is used by the authors in relation to a parallel robot as part of an aliquoting system.

 

The additional optimization seems to be introduced in a hasty way. A cad model of the final solution and its position in the robotic system is necessary to evaluate if the solution is applicable (obtained lengths seem a bit large comparing to other solutions explained in the introduction).

 

The workspace for the calculated optimal parameters was determined and a check was made that a cylinder with the calculated radius can be inscribed in it. The CAD model of the obtained solution was designed, obtained and used to analyze the relative position of the robots in the system. The dimensions of the final solution can be refined based on additional optimization that takes into account dynamic characteristics. However, the authors are confident that it will be based on the research carried out in the framework of the current work. They represent a self-sufficient work, including methods, algorithms and a software package for analyzing the geometric aspects of optimization.

Reviewer 3 Report

After carefully rereading this work, I cannot approve it for publication. It appears that the authors have done limited work towards improving their manuscript and several of my comments have been ignored. Therefore, I am forced to repeat many of my previous comments here. I still recommend to revise and resubmit the manuscript, until all major issues raised have been satisfactorily addressed (or proven to be not relevant, should that be the case).

ISSUES ALREADY OBSERVED IN THE FIRST ROUND OF REVIEWS
1)    Many details are provided on laboratory practice for analysis of biological samples, together with bibliographic references, yet the actual content is on the workspace analysis of a robot that could be applied to many other fields. In my previous review, I noted that the connection of this work with the COVID19 pandemic appears scarcely relevant. In their rebuttal, the authors state that "The development of a system for aliquoting (biosample analysis) is very relevant in connection with COVID19 from a practical point of view": this, then, should be explained in the manuscript, with supporting references. Similarly, the claim that robotization "[...] eliminates the time-consuming operation to separate the blood clot from the serum by the operator [...]" (see rebuttal, point 1) should be explained in the manuscript; the reference to [3] (page 1 of the manuscript) appears irrelevant, as robots are nowhere cited in the online reference linked. In brief, the goal of developing "an intelligent robotic system that considers the variation in the volume of the initial samples and the presence of different phases of liquid in them" (page 2) does not appear to have been reached: for instance, it would also be necessary to present the control system of the robot and show how it can guarantee that blood clots will maintain their integrity during manipulation of test tubes.
2)    No experimental results are provided; the design of the parallel robot under exam is only sketched, by finding its dimensions, and no CAD model is presented. In my previous review, I noted that this robot uses the classical "Delta" architecture, which has been studied since the '80s. In their rebuttal, the authors state that "the novelty of the technical solution presented in this article lies in the fact that an excavating head supplements this mechanism with an electromechanical drive, which was designed by the authors": it is then unclear whether the topic of the manuscript is the manipulator (as indicated by the title) or the excavating head. If the focus is on the manipulator, many details on pipetting devices could be omitted; if the focus is instead on the head, the discussion on the manipulator workspace is irrelevant. Finally, if "The DeLi robot is based on the existing Delta-type mechanism" (see rebuttal, point 5), why not simply call it a Delta robot, instead of introducing a new name?
3)    Out of 40 references, 12 are from at least one of the authors, but their relevance appears questionable. See for instance Ref. [2]: how are epidemiological models relevant here?
4)    After the workspace analysis, the kinematic parameters of the robot are optimized. This is achieved, from what I understand (the description on pages 17-18 appears vague), through trial-and-error. Thus, it is unlikely that the globally optimal architecture has been found; compare this approach with the state of the art on multi-variable, multi-objective optimization algorithms available in the literature. Moreover, the optimization only appears to consider the workspace volume, while a robust design must take into account several other parameters (such as kinematic and dynamic performance, error transmission, stiffness and so on): optimizing exclusively for workspace volume easily leads to designs that are in fact poor when considering other desirable characteristics. In their rebuttal, the authors state that "the task was to investigate the influence of singularity zones and interference of links, which significantly reduce the workspace, including in accordance with the technological process of aliquoting, which is important to consider when designing such structures". However, I do not understand how the aliquoting process influences the workspace analysis; in any case, all the other design parameters mentioned above have been ignored. Finally, I do not understand how a singularity surface (which is two-dimensional) can "reduce" a workspace (which is a 3D volume); see Table 1.
5)     In my previous review, I noted that the algorithm in Section 3 to approximate the workspace is similar to interval analysis (see "Introduction to interval analysis", R. E. Moore et al., SIAM, 2009). In their rebuttal, the authors state that "The workspace analysis is based on the well-known methods of interval analysis, however, using the algorithm for determining the interference of links developed by the authors": it is then necessary to reference and discuss the existing bibliography on interval analysis. This however reduces the novelty of the contribution, which is essentially an application of well-known techniques to the analysis of a robot architecture (which is not novel, either).

OTHER ISSUES
A)    The variables x_P, y_P and z_P, used from page 7 onward, are not defined in the text.
B)    An additional optimization was added at the end of the article. However, the assumptions appear questionable: why is the volume inscribed within the workspace assumed to be cylindrical? Why is it of interest to maximize the radius r_c of said volume? Notice that the desired workspace for the pipetting task at hand will not in general be cylindrical; moreover, its global dimensions are known, so further increasing the effective workspace beyond these requirements does not seem useful. In the revised manuscript, the authors state that "We can conclude that the manipulator workspace is round based on the previous analysis": where has this been shown? The workspaces presented in Figures 11 and 14 are clearly not cylindrical. Finally, the results of this second optimization (page 19, line 484) seem to be at odds with the results of the first one (page 18, line 452). I do not understand how this second optimization takes into account "the peculiarities of the aliquot problem" (see rebuttal, point 4).
C)    The list of references has been edited, per my suggestion, adding references on previous works on Delta parallel robots; however, no discussion of previous results is offered, as References 25-32 are barely mentioned. Also, in their rebuttal, the authors state that "In the existing works on the analysis of the workspace of the Delta mechanism, little attention is paid to the analysis of the influence of singularity zones and interference of the links", which is not the case. See for instance the following works:
    -    "Delta robot: inverse, direct, and intermediate Jacobians", M. López et al., 2006;
    -    "Singularity, isotropy, and velocity transmission evaluation of a three translational degrees-of-freedom parallel robot", Y. Zhao, 2013;
    -    "Kinetostatic Performance and Collision-free Workspace Analysis of a 3-DOF Delta Parallel Robot", P. Ataei et al., 2017.
D)    In their rebuttal, the authors state that "the novelty of the work in general is associated with the development of a new system consisting of several robots", yet only one robot (the Delta, which has a parallel architecture) is discussed. The serial collaborative arm visible in Figure 3 is instead barely mentioned and its role in the global design is unclear.
E)    It is claimed (page 4 of the manuscript) that the architecture presented offers superior "maneuverability within the workspace", which seems questionable: a parallel architecture, such as the one considered here, generally has lower maneuverability with respect to a serial alternative, due to the increased risk of link interference. Mentioning "a host of other advantages" is vague and unconvincing.
F)    Since the last round of reviews, "the additional kinematic circuit has been removed" (see rebuttal, point 5, and Figure 6 in the two versions of the manuscript). The alternative approach suggested in the rebuttal is to insert an electric drive inside the excavating head. This way, the central kinematic chain can be removed; however, the robot is no longer fully parallel and the inertia of said drive must be carried by the other motors, thus increasing torques and energy consumption.

Author Response

After carefully rereading this work, I cannot approve it for publication. It appears that the authors have done limited work towards improving their manuscript and several of my comments have been ignored. Therefore, I am forced to repeat many of my previous comments here. I still recommend to revise and resubmit the manuscript, until all major issues raised have been satisfactorily addressed (or proven to be not relevant, should that be the case).

 

ISSUES ALREADY OBSERVED IN THE FIRST ROUND OF REVIEWS

1)    Many details are provided on laboratory practice for analysis of biological samples, together with bibliographic references, yet the actual content is on the workspace analysis of a robot that could be applied to many other fields. In my previous review, I noted that the connection of this work with the COVID19 pandemic appears scarcely relevant. In their rebuttal, the authors state that "The development of a system for aliquoting (biosample analysis) is very relevant in connection with COVID19 from a practical point of view": this, then, should be explained in the manuscript, with supporting references. Similarly, the claim that robotization "[...] eliminates the time-consuming operation to separate the blood clot from the serum by the operator [...]" (see rebuttal, point 1) should be explained in the manuscript; the reference to [3] (page 1 of the manuscript) appears irrelevant, as robots are nowhere cited in the online reference linked. In brief, the goal of developing "an intelligent robotic system that considers the variation in the volume of the initial samples and the presence of different phases of liquid in them" (page 2) does not appear to have been reached: for instance, it would also be necessary to present the control system of the robot and show how it can guarantee that blood clots will maintain their integrity during manipulation of test tubes.

 

The authors shortened the description of laboratory practice for the analysis of biological samples. The relevance of the work in connection with the COVID 19 pandemic was also explained, a reference to the investigation was added [2]. A description of the aliquoting process has been added and it has been explained how the operator can reduce the laboriousness of the operation to separate the blood clot from the serum, and a reference to the source has been added. Reference to [3] has been removed.

 

2)    No experimental results are provided; the design of the parallel robot under exam is only sketched, by finding its dimensions, and no CAD model is presented. In my previous review, I noted that this robot uses the classical "Delta" architecture, which has been studied since the '80s. In their rebuttal, the authors state that "the novelty of the technical solution presented in this article lies in the fact that an excavating head supplements this mechanism with an electromechanical drive, which was designed by the authors": it is then unclear whether the topic of the manuscript is the manipulator (as indicated by the title) or the excavating head. If the focus is on the manipulator, many details on pipetting devices could be omitted; if the focus is instead on the head, the discussion on the manipulator workspace is irrelevant. Finally, if "The DeLi robot is based on the existing Delta-type mechanism" (see rebuttal, point 5), why not simply call it a Delta robot, instead of introducing a new name?

 

A CAD model of the investigated parallel robot was built to determine the robots' relative position and build the intersections of their workspaces. It was determined that the intersection area is sufficient to accommodate a medical rack with 96 tubes of fractionated biological fluid. In addition, the authors shortened the description of dispensing head. The emphasis of the work was focused on determining the workspace required to implement the aliquoting process. In this investigation, a standard delta robot with a dispensing head tool is used, but the designation DeLi is used by the authors in relation to a parallel robot as part of an aliquoting system.

 

3)    Out of 40 references, 12 are from at least one of the authors, but their relevance appears questionable. See for instance Ref. [2]: how are epidemiological models relevant here?

 

The list of references has been revised, the citation [2] has been removed.

 

4)    After the workspace analysis, the kinematic parameters of the robot are optimized. This is achieved, from what I understand (the description on pages 17-18 appears vague), through trial-and-error. Thus, it is unlikely that the globally optimal architecture has been found; compare this approach with the state of the art on multi-variable, multi-objective optimization algorithms available in the literature. Moreover, the optimization only appears to consider the workspace volume, while a robust design must take into account several other parameters (such as kinematic and dynamic performance, error transmission, stiffness and so on): optimizing exclusively for workspace volume easily leads to designs that are in fact poor when considering other desirable characteristics. In their rebuttal, the authors state that "the task was to investigate the influence of singularity zones and interference of links, which significantly reduce the workspace, including in accordance with the technological process of aliquoting, which is important to consider when designing such structures". However, I do not understand how the aliquoting process influences the workspace analysis; in any case, all the other design parameters mentioned above have been ignored. Finally, I do not understand how a singularity surface (which is two-dimensional) can "reduce" a workspace (which is a 3D volume); see Table 1.

 

The authors do not agree with the reviewers' comments that the aliquoting process does not affect the analysis of the workspace. The required range of vertical movement is calculated from the geometry of the pipettes and tubes used in the aliquoting process. The calculated range is directly used in optimizing the parameters of the Delta robot. The authors have already written that they agree with the reviewer's remark about the need to take into account dynamic characteristics. However, in this work, the task was to investigate the effect of singularity zones and interferences, which significantly reduce the workspace, including in accordance with the aliquoting process, which is important to consider when designing such structures. The aliquoting process, as described above, directly affects the analysis of the workspace by calculating the required range of vertical movements for optimization. Also, the authors have already answered that they do not agree with the reviewer's remark "how a singularity surface (which is two-dimensional) can "reduce" a workspace (which is a 3D volume)". The algorithms suggested by the reviewer for that allow a robot to pass through a singularity can be applied to serial robots or to some robots based on 5-bars architecture where it is possible to use the robot inertia to overcome the singularities. Delta robots can only be used in one of the two configurations.

 

5)     In my previous review, I noted that the algorithm in Section 3 to approximate the workspace is similar to interval analysis (see "Introduction to interval analysis", R. E. Moore et al., SIAM, 2009). In their rebuttal, the authors state that "The workspace analysis is based on the well-known methods of interval analysis, however, using the algorithm for determining the interference of links developed by the authors": it is then necessary to reference and discuss the existing bibliography on interval analysis. This however reduces the novelty of the contribution, which is essentially an application of well-known techniques to the analysis of a robot architecture (which is not novel, either).

 

Auhors referenced and discussed the existing bibliography on interval analysis on the page 4.

 

OTHER ISSUES

A) The variables x_P, y_P and z_P, used from page 7 onward, are not defined in the text.

 

Variables x_P, y_P, z_P have been defined in the text. It was stated that these coordinates are the center of the moving platform.

 

B) An additional optimization was added at the end of the article. However, the assumptions appear questionable: why is the volume inscribed within the workspace assumed to be cylindrical? Why is it of interest to maximize the radius r_c of said volume? Notice that the desired workspace for the pipetting task at hand will not in general be cylindrical; moreover, its global dimensions are known, so further increasing the effective workspace beyond these requirements does not seem useful. In the revised manuscript, the authors state that "We can conclude that the manipulator workspace is round based on the previous analysis": where has this been shown? The workspaces presented in Figures 11 and 14 are clearly not cylindrical. Finally, the results of this second optimization (page 19, line 484) seem to be at odds with the results of the first one (page 18, line 452). I do not understand how this second optimization takes into account "the peculiarities of the aliquot problem" (see rebuttal, point 4).

 

The authors have added to section 6 the rationale for choosing a cylindrical workspace. It is shown that with different dimensions of the Delta mechanism, the workspace has a round shape and the cylinder inscribed in the workspace will have a larger volume than the inscribed parallelepiped. The reviewer points out that "desired workspace for the pipetting task at hand will not in general be cylindrical". Most likely, this statement is due to the fact that most of the existing devices for aliquating have a parallelepiped shape. However, the use of a parallelepiped form of the workspace will imply the refusal to use the additional useful volume of the Delta robot's workspace segments. As part of the optimization, not only the maximization of the radius r_c is taken into account, but also the minimization of the size of the delta robot. The optimization criterion takes into account both of these conditions. The results of second optimization are different from the results of the first one. This is due to the fact that the criterion of the first optimization is the maximization of the volume of the workspace, and the criterion of the second optimization is the ratio of the sum of the dimensions of the delta robot and the radius of the cylinder that can be inscribed inside the workspace. In this case, the required height of this cylinder is calculated based on the requirements of aliquoting. (sizes).

 

C) The list of references has been edited, per my suggestion, adding references on previous works on Delta parallel robots; however, no discussion of previous results is offered, as References 25-32 are barely mentioned. Also, in their rebuttal, the authors state that "In the existing works on the analysis of the workspace of the Delta mechanism, little attention is paid to the analysis of the influence of singularity zones and interference of the links", which is not the case. See for instance the following works:

    -    "Delta robot: inverse, direct, and intermediate Jacobians", M. López et al., 2006;

    -    "Singularity, isotropy, and velocity transmission evaluation of a three translational degrees-of-freedom parallel robot", Y. Zhao, 2013;

    -    "Kinetostatic Performance and Collision-free Workspace Analysis of a 3-DOF Delta Parallel Robot", P. Ataei et al., 2017.

 

The authors agree with the reviewer's remark that in [M. López et al., 2006, Y. Zhao, 2013 and P. Ataei et al., 2017] attention is paid to the analysis of the influence of singularity zones and interference of the links. Nevertheless, the first two papers did not consider different configurations of the delta robot, the influence of singularity zones on the volume of the workspace. At the same time, the authors on page 13 cite the authors of the article [P. Ataei et al., 2017] and describe the shortcomings of this method for determining the interference of links:

"In [34], a similar condition is used, but the approach has drawbacks. In particular, the authors propose to determine the interference of the segments on the auxiliary plane, and not the distance between the nearest points. This does not allow identifying such an interference of links in which there is no interference of the axes."

 

D) In their rebuttal, the authors state that "the novelty of the work in general is associated with the development of a new system consisting of several robots", yet only one robot (the Delta, which has a parallel architecture) is discussed. The serial collaborative arm visible in Figure 3 is instead barely mentioned and its role in the global design is unclear.

 

The relative position of the Uni and DeLi robots and their workspaces was considered to test two requirements. The first is the sufficiency of the volume of the total workspace. A common workspace is required for placing racks with test tubes by the Uni robot in it, and then taking blood from them by the DeLi robot. The second requirement is that there are no collisions between robots when one of them works in a common workspace.

 

E) It is claimed (page 4 of the manuscript) that the architecture presented offers superior "maneuverability within the workspace", which seems questionable: a parallel architecture, such as the one considered here, generally has lower maneuverability with respect to a serial alternative, due to the increased risk of link interference. Mentioning "a host of other advantages" is vague and unconvincing.

 

Link interference was considered during workspace analysis and optimizing the parameters.

 

F) Since the last round of reviews, "the additional kinematic circuit has been removed" (see rebuttal, point 5, and Figure 6 in the two versions of the manuscript). The alternative approach suggested in the rebuttal is to insert an electric drive inside the excavating head. This way, the central kinematic chain can be removed; however, the robot is no longer fully parallel and the inertia of said drive must be carried by the other motors, thus increasing torques and energy consumption.

 

From the point of view of the constructive process, a more acceptable option turned out to be a dispensing head with an electric drive inside the dispensing head. The effect on inertia will be negligible since the drive rotation speeds and torque during the excavation process are small, and the motor has a small mass. In this regard, the cumbersome design of the additional kinematic chain was changed to the proposed, more technological version of the dispensing head with an integrated drive.

Round 3

Reviewer 3 Report

1. A figure has been added with a CAD model of the robot (Fig. 18, p. 19); however, this figure is hard to read and of low quality. In general, the figures are blurred and hard to read, especially when printed in black and white: see for instance Figures 8 and 12.
2. The design optimization is still performed through trial-and-error; a global optimization algorithm (see for instance genetic algorithms) could lead to better results.
3. Claiming that a singularity surface reduces the workspace volume is at least imprecise: it would be more correct to state that singularity surfaces separate the workspace into non-overlapping volumes. It is then necessary for the robot to remain within the same volume as it moves, in order to avoid crossing a singularity (which can be detrimental for robot control).
4. I do not see the need to introduce a new term (DeLi robot) for the Delta robot architecture, which is already well known. Also, "Delta robot" is generally written with a capital "D".
5. I suggest specifying on page 7 that the workspace analysis method is a direct application of interval analysis methods, as described in Refs. [28-31].
6. In their rebuttal, the authors admit that "The results of second optimization are different from the results of the first one.". Then, which one do they suggest to use in a practical design? It would be useful to compare the advantages and disadvantages of both optimal results.
7. The claim that "delta architectures are better suited for moving along curvilinear trajectories" should be justified.
8. The meaning of Table 2 is unclear in context.
9. More details could be added about how the workspace of the Uni robot is computed and about the method used to check against mutual interference between robots (page 18). Also, it would be necessary to add data about the dimensions and kinematic architecture of the Uni robot, together with the relative position of its fixed frame with respect to the Delta. How is multi-robot control performed here? 
10. Reference 9 (about tendon-driven robots) appears less relevant in context. Also, there is a typo in Ref. 10 ("ro[8bot").
11. References 25-32 are still barely mentioned. In my previous review, I mentioned three papers that appear relevant to this manuscript. The authors discuss the shortcomings of these previous works, but only in the rebuttal. More generally, I believe that a full bibliographic research on workspace analysis for translational robots should be included.

Author Response

A figure has been added with a CAD model of the robot (Fig. 18, p. 19); however, this figure is hard to read and of low quality. In general, the figures are blurred and hard to read, especially when printed in black and white: see for instance Figures 8 and 12.

The quality of the figures has been improved, the readability of the figures has been checked for black and white printing.

 

The design optimization is still performed through trial-and-error; a global optimization algorithm (see for instance genetic algorithms) could lead to better results.

Thank you for this valuable comment. The following text has been added. "A formal optimization algorithm will be planned as future for a further optimization of the obtained results"

 

Claiming that a singularity surface reduces the workspace volume is at least imprecise: it would be more correct to state that singularity surfaces separate the workspace into non-overlapping volumes. It is then necessary for the robot to remain within the same volume as it moves, in order to avoid crossing a singularity (which can be detrimental for robot control).

The authors agree with the comment. This paragraph is corrected.

 

I do not see the need to introduce a new term (DeLi robot) for the Delta robot architecture, which is already well known. Also, "Delta robot" is generally written with a capital "D".

As mentioned in the last round, this investigation uses a standard Delta robot with a tool in the form of a digging head, however, the DeLi term is used by the authors in relation to a parallel robot as part of the aliquoting system. The name of the Delta mechanism has been corrected (with a capital "D").

 

I suggest specifying on page 7 that the workspace analysis method is a direct application of interval analysis methods, as described in Refs. [28-31].

The authors added this sentence.

 

In their rebuttal, the authors admit that "The results of second optimization are different from the results of the first one.". Then, which one do they suggest to use in a practical design? It would be useful to compare the advantages and disadvantages of both optimal results.

Comparison of optimization results is added after Figure 17. The best configuration was chosen.

 

The claim that "delta architectures are better suited for moving along curvilinear trajectories" should be justified.

Added a sentence after this statement justifying this information, given the benefits of the Delta structure.

 

The meaning of Table 2 is unclear in context.

Additional information about Table 2 is added.

 

More details could be added about how the workspace of the Uni robot is computed and about the method used to check against mutual interference between robots (page 18).

Also, it would be necessary to add data about the dimensions and kinematic architecture of the Uni robot, together with the relative position of its fixed frame with respect to the Delta. How is multi-robot control performed here?

The Uni workspace is determined by the authors. Description of this added before figure 18 in the new version of the article. Information about the calculation of the workspace of the Uni manipulator has been added. Method (simulation in CAD system) used to check the interference between robots is also described. The scheme of the kinematic architecture of the Uni robot is presented in the article. The issues of multi-robot control are not considered in this article.

 

Reference 9 (about tendon-driven robots) appears less relevant in context. Also, there is a

typo in Ref. 10 ("ro[8bot").

The authors agree with the comments, the reference to source 9 has been removed, the typo in source 10 has been corrected.

 

References 25-32 are still barely mentioned. In my previous review, I mentioned three papers that appear relevant to this manuscript. The authors discuss the shortcomings of these previous works, but only in the rebuttal. More generally, I believe that a full bibliographic research on workspace analysis for translational robots should be included.

Bibliographic research on workspace analysis for translational robots is included after figure 3.