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Kinematics and Robot Design IV, KaRD2021

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A special issue of Robotics (ISSN 2218-6581).

Deadline for manuscript submissions: closed (15 November 2021) | Viewed by 40337

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Special Issue Editor

Prof. Dr. Raffaele Di Gregorio

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Guest Editor

Engineering Department, University of Ferrara, 44122 Ferrara, Italy
Interests: kinematics; dynamics; mechanism and machine theory; parallel manipulators; robot mechanics; biomechanics; vehicle mechanics; robotics
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Scientific Committee

- Massimo Callegari, Polytechnic University of Marche (Italy)
- Juan Antonio Carretero, University of New Brunswick (Canada)
- Yan Chen, Tianjin University (China)
- Daniel Condurache, “Gheorghe Asachi” Technical University of Iași (Romania)
- Xilun Ding, Beijing University of Aeronautics & Astronautics (China)
- Mary Frecker, Penn State - College of Engineering (USA)
- Clement Gosselin, Laval University (Canada)
- Just Herder, TU Deft (Netherlands)
- Larry Howell, Brigham Young University (USA)
- Xianwen Kong, Heriot-Watt University (UK)
- Pierre Larochelle, South Dakota School of Mines & Technology (USA)
- Giovanni Legnani, University of Brescia (Italy)
- Haitao Liu, Tianjin University (China)
- Daniel Martins, Universidade Federal de Santa Catarina (Brazil)
- Andreas Mueller, Johannes Kepler Universität (Austria)
- Andrew Murray, University of Dayton (USA)
- Leila Notash, Queen's University (Canada)
- Matteo Palpacelli, Polytechnic University of Marche (Italy)
- Alba Perez, Remy Robotics, Barcelona (Spain)
- Victor Petuya, University of the Basque Country (Spain)
- José Maria Rico Martinez, Universidad de Guanajuato (Mexico)
- Nina Robson, California State University, Fullerton (USA)
- Jon M. Selig, London South Bank University (UK)
- Bruno Siciliano, University of Naples Federico II (Italy)
- Tao Sun, Tianjin University (China)
- Yukio Takeda, Tokyo Institute of Technology (Japan)
- Federico Thomas, Institute of Industrial Robotics (Spain)
- Volkert Van Der Wijk, TU Deft (Netherlands)

Dear Colleagues,

KaRD2021 is the 4th issue of the KaRD series, hosted by MDPI’s Robotics. The KaRD series of open access Special Issues is characterized with low publication costs (CHF 400 author processing fee (APC) per paper), comparable with the registration fee of a small international congress. It started on 2018 and is now an open environment where researchers can present their works and discuss all the topics focused on the many aspects that involve kinematics in the design of robotic/automatic systems by also using supplementary multimedia materials uploadable during the submission. A “Scientific Committee”, comprised of researchers coming from all over the world, supports and supervises the Guest Editor activity. All the papers are peer reviewed as soon as they are submitted and, if accepted, immediately published on MDPI’s Robotics and appear on the website of the KaRD issue. Starting with this year, the papers of each KaRD issue are also collected into freely downloadable e-books, whose printed copy can also be ordered at a price that covers the printing costs.

Kinematics is intimately related to nearly all the design aspects of robotic/automatic systems. Topics like analysis and synthesis of mechanisms, robot modelling and simulation, robot control, mobility and singularity analysis, performance measures, accuracy analysis, path planning and obstacle avoidance, collaborative robotics, novel manipulator architectures, metamorphic mechanisms, compliant mechanism analysis and synthesis, micro/nano-manipulator design, origami-based robotics, medical and rehabilitation robotics, bioinspired robotics, etc., deal with kinematics. All these topics have a deep social impact and somehow delineate future perspectives of human welfare, which attract big economic interests

KaRD2021 provides a good opportunity for presenting research results that are immediately readable and usable by other researchers. In particular, submitting authors

- are able to also submit accompanying multimedia material;
- can request the “Open Peer Review” during the submission;
- are immediately able to upload, as a preprint on https://www.preprints.org/, the paper version submitted for review, where it will receive a DOI and will be readable/citable by other researchers;
- after the possible paper acceptance and the publication on Robotics, are able to upload their published paper on many social networks for researchers (e.g., ResearchGate.net), where they can publicly or privately interact with other researchers to start a discussion on the published results.

In short, KaRD series is an “agora”, where researchers efficiently exchange their experiences.

The Special Issue aims at collecting recent research on the following topics. Nevertheless, review papers are welcome, too.

Topics of interest include (but are not limited to):

Synthesis of mechanisms;
theoretical and computational kinematics;
robot modeling and simulation;
kinematics in robot control;
position analysis;
mobility and singularity analysis;
performance measures;
accuracy analysis;
path planning and obstacle avoidance;
novel manipulator architectures;
metamorphic mechanisms;
compliant mechanism analysis and synthesis;
micro/nanomanipulator design;
origami-based robotics;
medical and rehabilitation robotics;
kinematics in biological systems, humanoid robots and humanoid subsystems;
education in robotics.

Prof. Raffaele Di Gregorio
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Robotics is an international peer-reviewed open access quarterly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1400 CHF (Swiss Francs), but it is reduced to 400 CHF for the submission to this special issue. Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

mechanism synthesis
kinematic analysis
robot modeling and simulation
robot control
singularity analysis
performance measures
accuracy analysis
path planning
parallel manipulator
serial manipulator
robot design
compliant mechanism
micro/nanomanipulator
origami
medical and rehabilitation robotics
biomechanics

Related Special Issues

Kinematics and Robot Design V, KaRD2022 in Robotics (13 articles)
Kinematics and Robot Design VI, KaRD2023 in Robotics (10 articles)
Kinematics and Robot Design I, KaRD2018 in Robotics (14 articles)
Kinematics and Robot Design II, KaRD2019 in Robotics (7 articles)
Kinematics and Robot Design III, KaRD2020 in Robotics (10 articles)

Published Papers (12 papers)

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Research

21 pages, 1988 KiB

Open AccessArticle

Kinematic Model Pruning: A Design Optimization Technique for Simultaneous Optimization of Topology and Geometry

by Hannes Gamper, Adrien Luthi, Hubert Gattringer, Andreas Mueller and Mario Di Castro

Robotics 2022, 11(2), 31; https://doi.org/10.3390/robotics11020031 - 04 Mar 2022

Viewed by 2407

Abstract

This paper presents a method of optimizing the design of robotic manipulators using a novel kinematic model pruning technique. The optimization departs from an predefined candidate linkage consisting of a initial topology and geometry. It allows simultaneously optimizing the degree of freedom, the link lengths and other kinematic or dynamic performance criteria, while enabling the manipulator to follow the desired end-effector position and avoid collisions with the environment or itself. Current methods for design optimization rely on dedicated and complex frameworks, and solve the design optimization only as decoupled from each other in separate optimization problems. The proposed method only requires the introduction of a simple function, called a pruning function, as an objective function of an optimization problem. The introduced pruning function transforms a discrete topology optimization problem into a continuous problem that then can be solved simultaneously with other continuous objectives, using readily available optimization schemes. Two applications are presented: the optimization of a manipulator for the inspection of radio frequency cavities and a manipulator for maintenance within the future circular collider (FCC). Full article

(This article belongs to the Special Issue Kinematics and Robot Design IV, KaRD2021)

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20 pages, 2306 KiB

Open AccessArticle

Six-Bar Linkage Models of a Recumbent Tricycle Mechanism to Increase Power Throughput in FES Cycling

by Nicholas A. Lanese, David H. Myszka, Anthony L. Bazler and Andrew P. Murray

Robotics 2022, 11(1), 26; https://doi.org/10.3390/robotics11010026 - 11 Feb 2022

Cited by 1 | Viewed by 3273

Abstract

This paper presents the kinematic and static analysis of two mechanisms to improve power throughput for persons with tetra- or paraplegia pedaling a performance tricycle via FES. FES, or functional electrical stimulation, activates muscles by passing small electrical currents through the muscle creating a contraction. The use of FES can build muscle in patients, relieve soreness, and promote cardiovascular health. Compared to an able-bodied rider, a cyclist stimulated via FES produces an order of magnitude less power creating some notable pedaling difficulties especially pertaining to inactive zones. An inactive zone occurs when the leg position is unable to produce enough power to propel the tricycle via muscle stimulation. An inactive zone is typically present when one leg is fully bent and the other leg is fully extended. Altering the motion of a cyclist’s legs relative to the crank position can potentially reduce inactive zones and increase power throughput. Some recently marketed bicycles showcase pedal mechanisms utilizing alternate leg motions. This work considers performance tricycle designs based on the Stephenson III and Watt II six-bar mechanisms where the legs define two of the system’s links. The architecture based on the Stephenson III is referred to throughout as the CDT due to the legs’ push acting to coupler-drive the four-bar component of the system. The architecture based on the Watt II is referred to throughout as the CRT due to the legs’ push acting to drive the rocker link of the four-bar component of the system. The unmodified or traditional recumbent tricycle (TRT) provides a benchmarks by which the designs proposed herein may be evaluated. Using knee and hip torques and angular velocities consistent with a previous study, this numerical study using a quasi-static power model of the CRT suggests a roughly 50% increase and the CDT suggests roughly a doubling in average crank power, respectively, for a typical FES cyclist. Full article

(This article belongs to the Special Issue Kinematics and Robot Design IV, KaRD2021)

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16 pages, 4719 KiB

Open AccessArticle

Mixed Position and Twist Space Synthesis of 3R Chains

by Neda Hassanzadeh and Alba Perez-Gracia

Robotics 2022, 11(1), 13; https://doi.org/10.3390/robotics11010013 - 10 Jan 2022

Cited by 2 | Viewed by 2407

Abstract

Mixed-position kinematic synthesis is used to not only reach a certain number of precision positions, but also impose certain instantaneous motion conditions at those positions. In the traditional approach, one end-effector twist is defined at each precision position in order to achieve better guidance of the end-effector along a desired trajectory. For one-degree-of-freedom linkages, that suffices to fully specify the trajectory locally. However, for systems with a higher number of degrees of freedom, such as robotic systems, it is possible to specify a complete higher-dimensional subspace of potential twists at particular positions. In this work, we focus on the 3R serial chain. We study the three-dimensional subspaces of twists that can be defined and set the mixed-position equations to synthesize the chain. The number and type of twist systems that a chain can generate depend on the topology of the chain; we find that the spatial 3R chain can generate seven different fully defined twist systems. Finally, examples of synthesis with several fully defined and partially defined twist spaces are presented. We show that it is possible to synthesize 3R chains for feasible subspaces of different types. This allows a complete definition of potential motions at particular positions, which could be used for the design of precise interaction with contact surfaces. Full article

(This article belongs to the Special Issue Kinematics and Robot Design IV, KaRD2021)

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16 pages, 3963 KiB

Open AccessArticle

Design of a Labriform-Steering Underwater Robot Using a Multiphysics Simulation Environment

by Daniele Costa, Cecilia Scoccia, Matteo Palpacelli, Massimo Callegari and David Scaradozzi

Robotics 2022, 11(1), 11; https://doi.org/10.3390/robotics11010011 - 07 Jan 2022

Cited by 3 | Viewed by 3581

Abstract

Bio-inspired solutions devised for Autonomous Underwater Robots are currently investigated by researchers as a source of propulsive improvement. To address this ambitious objective, the authors have designed a carangiform swimming robot, which represents a compromise in terms of efficiency and maximum velocity. The requirements of stabilizing a course and performing turns were not met in their previous works. Therefore, the aim of this paper is to improve the vehicle maneuvering capabilities by means of a novel transmission system capable of transforming the constant angular velocity of a single rotary actuator into the pitching–yawing rotation of fish pectoral fins. Here, the biomimetic thrusters exploit the drag-based momentum transfer mechanism of labriform swimmers to generate the necessary steering torque. Aside from inertia and encumbrance reduction, the main improvement of this solution is the inherent synchronization of the system granted by the mechanism’s kinematics. The system was sized by using the experimental results collected by biologists and then integrated in a multiphysics simulation environment to predict the resulting maneuvering performance. Full article

(This article belongs to the Special Issue Kinematics and Robot Design IV, KaRD2021)

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17 pages, 4371 KiB

Open AccessEditor’s ChoiceArticle

Dimensional Synthesis of a Novel 3-URU Translational Manipulator Implemented through a Novel Method

by Raffaele Di Gregorio

Robotics 2022, 11(1), 10; https://doi.org/10.3390/robotics11010010 - 05 Jan 2022

Cited by 2 | Viewed by 2454

Abstract

A dimensional synthesis of parallel manipulators (PMs) consists of determining the values of the geometric parameters that affect the platform motion so that a useful workspace with assigned sizes can be suitably located in a free-from-singularity region of its operational space. The main goal of this preliminary dimensioning is to keep the PM far enough from singularities to avoid high internal loads in the links and guarantee a good positioning precision (i.e., for getting good kinematic performances). This paper presents a novel method for the dimensional synthesis of translational PMs (TPMs) and applies it to a TPM previously proposed by the author. The proposed method, which is based on Jacobians’ properties, exploits the fact that TPM parallel Jacobians are block diagonal matrices to overcome typical drawbacks of indices based on Jacobian properties. The proposed method can be also applied to all the lower-mobility PMs with block diagonal Jacobians that separate platform rotations from platform translations (e.g., parallel wrists). Full article

(This article belongs to the Special Issue Kinematics and Robot Design IV, KaRD2021)

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13 pages, 7275 KiB

Open AccessCommunication

A Methodology for Flexible Implementation of Collaborative Robots in Smart Manufacturing Systems

by Hermes Giberti, Tommaso Abbattista, Marco Carnevale, Luca Giagu and Fabio Cristini

Robotics 2022, 11(1), 9; https://doi.org/10.3390/robotics11010009 - 04 Jan 2022

Cited by 15 | Viewed by 4808

Abstract

Small-scale production is relying more and more on personalization and flexibility as an innovation key for success in response to market needs such as diversification of consumer preferences and/or greater regulatory pressure. This can be possible thanks to assembly lines dynamically adaptable to new production requirements, easily reconfigurable and reprogrammable to any change in the production line. In such new automated production lines, where traditional automation is not applicable, human and robot collaboration can be established, giving birth to a kind of industrial craftsmanship. The idea at the base of this work is to take advantage of collaborative robotics by using the robots as other generic industrial tools. To overcome the need of complex programming, identified in the literature as one of the main issues preventing cobot diffusion into industrial environments, the paper proposes an approach for simplifying the programming process while still maintaining high flexibility through a pyramidal parametrized approach exploiting cobot collaborative features. An Interactive Refinement Programming procedure is described and validated through a real test case performed as a pilot in the Building Automation department of ABB in Vittuone (Milan, Italy). The key novel ingredients in this approach are a first translation phase, carried out by engineers of production processes who convert the sequence of assembly operations into a preliminary code built as a sequence of robot operations, followed by an on-line correction carried out by non-expert users who can interact with the machine to define the input parameters to make the robotic code runnable. The users in this second step do not need any competence in programming robotic code. Moreover, from an economic point of view, a standardized way of assessing the convenience of the robotic investment is proposed. Both economic and technical results highlight improvements in comparison to the traditional automation approach, demonstrating the possibility to open new further opportunities for collaborative robots when small/medium batch sizes are involved. Full article

(This article belongs to the Special Issue Kinematics and Robot Design IV, KaRD2021)

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34 pages, 4907 KiB

Open AccessArticle

A Screw Theory Approach to Computing the Instantaneous Rotation Centers of Indeterminate Planar Linkages

by Juan Ignacio Valderrama-Rodríguez, José M. Rico, J. Jesús Cervantes-Sánchez and Ricardo García-García

Robotics 2022, 11(1), 6; https://doi.org/10.3390/robotics11010006 - 31 Dec 2021

Cited by 2 | Viewed by 2472

Abstract

This paper presents a screw theory approach for the computation of the instantaneous rotation centers of indeterminate planar linkages. Since the end of the 19th century, the determination of the instantaneous rotation, or velocity centers of planar mechanisms has been an important topic in kinematics that has led to the well-known Aronhold–Kennedy theorem. At the beginning of the 20th century, it was found that there were planar mechanisms for which the application of the Aronhold–Kennedy theorem was unable to find all the instantaneous rotation centers (IRCs). These mechanisms were denominated complex or indeterminate. The beginning of this century saw a renewed interest in complex or indeterminate planar mechanisms. In this contribution, a new and simpler screw theory approach for the determination of indeterminate rotation centers of planar linkages is presented. The new approach provides a simpler method for setting up the equations. Furthermore, the algebraic equations to be solved are simpler than the ones published to date. The method is based on the systematic application of screw theory, isomorphic to the Lie algebra,

s e (3)

, of the Euclidean group,

S E (3)

, and the invariant symmetric bilinear forms defined on

s e (3)

. Full article

(This article belongs to the Special Issue Kinematics and Robot Design IV, KaRD2021)

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38 pages, 15554 KiB

Open AccessArticle

Development and Usability Testing of a Finger Grip Enhancer for the Elderly

by Dominic Wen How Tan, Poh Kiat Ng, Ervina Efzan Mhd Noor, Adi Saptari, Chee Chen Hue and Yu Jin Ng

Robotics 2022, 11(1), 5; https://doi.org/10.3390/robotics11010005 - 30 Dec 2021

Cited by 4 | Viewed by 3577

Abstract

As people age, their finger function deteriorates due to muscle, nerve, and brain degeneration. While exercises might delay this deterioration, an invention that enhances elderly people’s pinching abilities is essential. This study aims to design and develop a finger grip enhancer that facilitates the day-to-day pinching activities of elderly people. This research is an extension of a previous study that conceptualised a finger grip enhancer. The device facilitates finger flexion on the thumb and index finger, and weighs 520 g, allowing for improved portability and sufficient force exertion (13.9 N) for day-to-day pinching. To test for usability, eleven subjects aged 65 years and above performed a pinch-lift-hold test on various household objects. The pinch force before and after utilising the device was measured. Using Minitab 18, the statistical significance of using this device was analysed with a paired-samples t-test. With this device, the elderly people’s pinching abilities significantly improved in both pinch force and pinch force steadiness (p < 0.05). The proposed device has the potential to enhance elderly people’s quality of life by supporting a firm pinch in the handling of everyday objects. This research has applicational value in developing exoskeleton devices for patients who require rehabilitation. Full article

(This article belongs to the Special Issue Kinematics and Robot Design IV, KaRD2021)

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18 pages, 1538 KiB

Open AccessArticle

Multi-Domain Dynamic Modelling of a Low-Cost Upper Limb Rehabilitation Robot

by Adam G. Metcalf, Justin F. Gallagher, Andrew E. Jackson and Martin C. Levesley

Robotics 2021, 10(4), 134; https://doi.org/10.3390/robotics10040134 - 15 Dec 2021

Cited by 5 | Viewed by 2971

Abstract

Tracking patient progress through a course of robotic tele-rehabilitation requires constant position data logging and comparison, alongside periodic testing with no powered assistance. The test data must be compared with previous test attempts and an ideal baseline, for which a good understanding of the dynamics of the robot is required. The traditional dynamic modelling techniques for serial chain robotics, which involve forming and solving equations of motion, do not adequately describe the multi-domain phenomena that affect the movement of the rehabilitation robot. In this study, a multi-domain dynamic model for an upper limb rehabilitation robot is described. The model, built using a combination of MATLAB, SimScape, and SimScape Multibody, comprises the mechanical electro-mechanical and control domains. The performance of the model was validated against the performance of the robot when unloaded and when loaded with a human arm proxy. It is shown that this combination of software is appropriate for building a dynamic model of the robot and provides advantages over the traditional modelling approach. It is demonstrated that the responses of the model match the responses of the robot with acceptable accuracy, though the inability to model backlash was a limitation. Full article

(This article belongs to the Special Issue Kinematics and Robot Design IV, KaRD2021)

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22 pages, 1850 KiB

Open AccessArticle

Modal Kinematic Analysis of a Parallel Kinematic Robot with Low-Stiffness Transmissions

by Paolo Righettini, Roberto Strada and Filippo Cortinovis

Robotics 2021, 10(4), 132; https://doi.org/10.3390/robotics10040132 - 10 Dec 2021

Cited by 10 | Viewed by 2979

Abstract

Several industrial robotic applications that require high speed or high stiffness-to-inertia ratios use parallel kinematic robots. In the cases where the critical point of the application is the speed, the compliance of the main mechanical transmissions placed between the actuators and the parallel kinematic structure can be significantly higher than that of the parallel kinematic structure itself. This paper deals with this kind of system, where the overall performance depends on the maximum speed and on the dynamic behavior. Our research proposes a new approach for the investigation of the modes of vibration of the end-effector placed on the robot structure for a system where the transmission’s compliance is not negligible in relation to the flexibility of the parallel kinematic structure. The approach considers the kinematic and dynamic coupling due to the parallel kinematic structure, the system’s mass distribution and the transmission’s stiffness. In the literature, several papers deal with the dynamic vibration analysis of parallel robots. Some of these also consider the transmissions between the motors and the actuated joints. However, these works mainly deal with the modal analysis of the robot’s mechanical structure or the displacement analysis of the transmission’s effects on the positioning error of the end-effector. The discussion of the proposed approach takes into consideration a linear delta robot. The results show that the system’s natural frequencies and the directions of the end-effector’s modal displacements strongly depend on its position in the working space. Full article

(This article belongs to the Special Issue Kinematics and Robot Design IV, KaRD2021)

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16 pages, 7621 KiB

Open AccessArticle

Bio-Inspired Conceptual Mechanical Design and Control of a New Human Upper Limb Exoskeleton

by Narek Zakaryan, Mikayel Harutyunyan and Yuri Sargsyan

Robotics 2021, 10(4), 123; https://doi.org/10.3390/robotics10040123 - 12 Nov 2021

Cited by 4 | Viewed by 3328

Abstract

Safe operation, energy efficiency, versatility and kinematic compatibility are the most important aspects in the design of rehabilitation exoskeletons. This paper focuses on the conceptual bio-inspired mechanical design and equilibrium point control (EP) of a new human upper limb exoskeleton. Considering the upper limb as a multi-muscle redundant system, a similar over-actuated but cable-driven mechatronic system is developed to imitate upper limb motor functions. Additional torque adjusting systems at the joints allow users to lift light weights necessary for activities of daily living (ADL) without increasing electric motor powers of the device. A theoretical model of the “ideal” artificial muscle exoskeleton is also developed using Hill’s natural muscle model. Optimal design parameters of the exoskeleton are defined using the differential evolution (DE) method as a technique of a multi-objective optimization. The proposed cable-driven exoskeleton was then fabricated and tested on a healthy subject. Results showed that the proposed system fulfils the desired aim properly, so that it can be utilized in the design of rehabilitation robots. Further studies may include a spatial mechanism design, which is especially important for the shoulder rehabilitation, and development of reinforcement learning control algorithms to provide more efficient rehabilitation treatment. Full article

(This article belongs to the Special Issue Kinematics and Robot Design IV, KaRD2021)

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14 pages, 2137 KiB

Open AccessArticle

Kinematic Synthesis and Analysis of the RoboMech Class Parallel Manipulator with Two Grippers

by Zhumadil Baigunchekov, Med Amine Laribi, Azamat Mustafa and Abzal Kassinov

Robotics 2021, 10(3), 99; https://doi.org/10.3390/robotics10030099 - 03 Aug 2021

Cited by 3 | Viewed by 3107

Abstract

In this paper, methods of kinematic synthesis and analysis of the RoboMech class parallel manipulator (PM) with two grippers (end effectors) are presented. This PM is formed by connecting two output objects (grippers) with a base using two passive and one negative closing kinematic chains (CKCs). A PM with two end effectors can be used for reloading operations of stamped products between two adjacent main technologies in a cold stamping line. Passive CKCs represent two serial manipulators with two degrees of freedom, and negative CKC is a three-joined link with three negative degrees of freedom. A negative CKC imposes three geometric constraints on the movements of the two output objects. Geometric parameters of the negative CKC are determined on the basis of the problems of the Chebyshev and least-square approximations. Problems of positions and analogues of velocities and accelerations of the PM with two end effectors have been solved. Full article

(This article belongs to the Special Issue Kinematics and Robot Design IV, KaRD2021)

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