Closed Kinematic Chains Research Articles

Structural – parametric synthesis of a parallel manipulator with two grips

This paper describes the methods of structural-parametric synthesis of a parallel manipulator PM with two grippers, which can be used for reloading operations between two adjacent main technological equipment in a cold stamping technological line. This PM is formed by connecting two grippers end – effectors with a base using two passive and one negative closing kinematic chains (CKC).

CO191 Improving Shooting Accuracy and Center of Gravity with Closed Kinematic Chain Exercises in Handball Players

CO191 Improving Shooting Accuracy and Center of Gravity with Closed Kinematic Chain Exercises in Handball Players

Research on Collaboration Motion Planning Method for a Dual-Arm Robot Based on Closed-Chain Kinematics

Aiming to address challenges in the motion coordination of dual-arm robot engineering applications, a comprehensive set of planning methods is devised. This paper takes a dual-arm system composed of two six-degrees-of-freedom industrial robots as the research object. Initially, a transformation model is established for the characteristic trajectories between the workpiece coordinate system and various other coordinate systems. Subsequently, the position and orientation curves of the working trajectory are discretized to facilitate the controller’s execution. Furthermore, an analysis is conducted of the closed-chain kinematics relationship between two arms of the robot and a pose-calibration method based on a reference coordinate system is introduced. Finally, constraints to the collaborative motion of the dual-arm robot are analyzed, leading to the establishment of a motion collaboration planning methodology. Simulations and experiments demonstrate that the proposed approach enables effective and collaborative task planning for dual-arm robots. Moreover, joint angle and angular velocity curves corresponding to the motion trajectory exhibit smoothness, reducing joint impacts.

THE EFFECT OF LOWER EXTREMITY CLOSED KINEMATICS CHAIN EXERCISE ON POLYCYSTIC OVARIAN SYNDROME WITH MENORRHEA

Aim:This study investigated the effect of lower extremity closed kinematics chain exercise on polycystic ovarian syndrome with menorrhea. Method:A total of 35 subject young women with polycystic ovarian syndrome between the age of 18 to 30 years, were recruited over 6 months and randomly allocated to an intervention group(n=35), participated in this observational experimental study. In this study menorrhea flow were measured at baseline prior to enrolment after 6 months of participation. In an intention-to-treat analysis, we experiment the closed kinematics chain exercise is effective in polycystic ovarian syndrome with menorrhea. Result: Result of this study were analysed in terms effect of lower extremity closed kinematics chain exercise on menorrhea with polycystic ovarian syndrome patient the population of 35 subjects [all females] were served for effect of lower extremity of closed kinematics exercise on patients with menorrhea in polycystic ovarian syndrome in age group of 18 to 30 yrs. Out of 35 patients Pads count are compared between pre and post result and same in result is seen in Menorrhea outcome questionnaire score. The study states that pads count and menorrhea outcome questionnaire score for menorrhea in polycystic ovarian syndrome patient is showed that improve after lower extremities closed kinematics chain exercise. Conclusion: The study concluded that conventional physiotherapy with lower extremity closed kinematics chain exercises are effective in reducing menorrhea in patient with polycystic ovarian syndrome.

Sampling-Based Global Path Planning Using Convex Polytope Approximation for Narrow Collision-Free Space of Humanoid

In this paper, we propose a computationally fast method of sampling-based global path planning for humanoids under Manifold Constraints such as closed kinematic chains and Volume-Reducing Constraints such as collision avoidance. In multi-contact and whole-body manipulation of humanoids, narrow collision-free space causes path planning to take a long computation time (narrow corridor problem). In previous research of constrained planning, Manifold Constraints are locally approximated by tangent plane, and steering motions along Manifold Constraints are found efficiently by projection or continuation methods. In this paper, we applied constrained planning algorithms to collision avoidance. Since tangent plane cannot approximate Volume-Reducing Constraints, we adopted convex polytope instead of tangent plane. Both Manifold Constraints and Volume-Reducing Constraints are locally approximated by convex polytope with linear equality and inequality constraints, and steering motions inside the convex polytope are found efficiently by the SQP-based prioritized inverse kinematics. We developed CP-KPIECE (Convex Polytope approximation-based KPIECE) with this approach. Benchmarks using the humanoid JAXON proved the effectiveness of our approach for fast path planning in narrow collision-free space of humanoids.

Kinematic modeling and simultaneous calibration for acupuncture robot

Acupuncture robot is a new-era product combining traditional acupuncture and cutting-edge technology. The calibration of the vision system and the acupuncture mechanism is a crucial prerequisite for humanoid acupuncture control, which has not yet been explored. In this paper, a simultaneous offline calibration method is proposed for acupuncture robots. Analysis reveals that its calibration problem is defined with three closed kinematic chains, while the typical problems cover only a single chain. Decoupling them, a Kronecker product-based method is deduced to access the closed-form rotation component. As opposed to quaternion-based methods, it only experiences linear complexity in sign ambiguity, which can produce a more precise solution in finite time. Further, a simultaneous optimization model that encompasses all components is established, which can be solved with stochastic gradient descent-based methods. It is free of truncation errors and thus has higher calibration accuracy and convergence speed. Besides, the impairment in error propagation between different closed kinematic chains is mitigated compared to step-by-step methods. Finally, simulations and experiments are carried out. Notably, the proposed method can be easily extended to other robot calibration problems with multiple closed kinematic chains.

A Flexible MATLAB/Simulink Simulator for Robotic Floating-base Systems in Contact with the Ground: Theoretical Background and Implementation Details

This paper presents an open-source MATLAB/Simulink physics simulator for rigid-body articulated systems, including manipulators and floating-base robots. Thanks to MATLAB/Simulink features like MATLAB system classes and Simulink Function blocks, the presented simulator combines a programmatic and block-based approach, resulting in a flexible design in the sense that different parts, including its physics engine, robot-ground interaction model, and state evolution algorithm are simply accessible and editable. Moreover, through the use of Simulink dynamic mask blocks, the proposed simulator supports robot models integrating open-chain and closed-chain kinematics with any desired number of links interacting with the ground. This simulator can also integrate second-order actuator dynamics. Furthermore, the simulator benefits from a one-line installation and an easy-to-use Simulink interface.

Calibration of link errors in rotary axes of five-axis machine tools using a six-dimensional motion measuring device

In this study, the position-independent geometric errors (PIGEs) of five-axis machine tools are identified and calibrated using a Stewart–Gough platform (SGP) based Motion Measuring Device (MMD). As the MMD of micrometer-level accuracy is cable of six-dimensional pose measurements, a closed kinematic chain is established by installing the upper and lower plate of the MMD to the spindle and rotary worktable of the machine tool, respectively. Particularly, the sensor-mounting misalignments, which are inevitable but mostly ignored in the previous PIGE identification methods, are formulated and identified together with the PIGEs. Thus, the sensor-mounting misalignments will not affect the accuracy of PIGE calibration. The proposed method is verified by simulation and experimental results. The synchronous motion test (SMT) demonstrates that the five-axis machine tool owns a high accuracy of 5 micrometers in the tested motion range after PIGE calibration.

Kinematic model calibration of a collaborative redundant robot using a closed kinematic chain

In this paper, we propose a novel approach for the kinematic calibration of collaborative redundat robots, focusing on improving their precision using a cost-effective and efficient method. We exploit the redundancy of the closed-loop kinematic chain by utilizing a spherical joint, enabling precise definition of the robot end-effector position while maintaining free joint motion in the null space. Leveraging the availability of joint torque sensors in most collaborative robots, we employ a kinesthetic approach to obtain constrained joint motion for calibration. An optimization approach is utilized to determine the optimal kinematic parameters based on measured joint positions and a constrained end-effector position defined by the spherical joint. The effectiveness of the proposed method is demonstrated and validated on the Franka Emika Panda robot, a 7-DoF robot. Results indicate a significant enhancement in absolute accuracy, with comparable performance to more expensive sensor systems such as optical measurement systems. Our approach offers a practical and cost-effective solution for improving the precision of collaborative robots.

Task Location to Improve Human–Robot Cooperation: A Condition Number-Based Approach

This paper proposes and implements an approach to evaluate human–robot cooperation aimed at achieving high performance. Both the human arm and the manipulator are modeled as a closed kinematic chain. The proposed task performance criterion is based on the condition number of this closed kinematic chain. The robot end-effector is guided by the human operator via an admittance controller to complete a straight-line segment motion, which is the desired task. The best location of the selected task is determined by maximizing the minimum of the condition number along the path. The performance of the proposed approach is evaluated using a criterion related to ergonomics. The experiments are executed with several subjects using a KUKA LWR robot to repeat the specified motion to evaluate the introduced approach. A comparison is presented between the current proposed approach and our previously implemented approach where the task performance criterion was based on the manipulability index of the closed kinematic chain. The results reveal that the condition number-based approach improves the human–robot cooperation in terms of the achieved accuracy, stability, and human comfort, but at the expense of task speed and completion time. On the other hand, the manipulability-index-based approach improves the human–robot cooperation in terms of task speed and human comfort, but at the cost of the achieved accuracy.

Synchronous Sliding Mode Control for a 4-DOF Parallel Manipulator in Practice

This paper proposes a synchronous sliding mode control (SSMC) method for a 4-DOF parallel robot model in practice with the influence of uncertain dynamics such as friction, external noise, and model error. A closed kinematic chain structure characterizes the parallel robot. The moving platform is controlled by four kinematic chains working together to follow a predetermined trajectory. However, traditional control methods only control each joint individually; if one of the actuators fails or has an external force, it can lead to system breakdown. Therefore, synchronous control to coordinate the operation of the arms is necessary. The synchronization algorithm is characterized by the cross-coupling error, which is the combination of tracking and synchronization errors for the system to achieve the synchronization goal. Cross-coupling error is used to design the sliding surface of the SSMC. The advantages of sliding mode control (SMC) are that it resists the influence of uncertain dynamics and it is combined with the synchronization algorithm. A control law is developed based on the sliding surface to ensure simultaneous convergence of both tracking and synchronization errors towards zero. The stability of the system is proven using the Lyapunov theory. In order to verify the effectiveness of the proposed approach, a 4-DOF parallel robot testbench is constructed. The SSMC controller results are compared with the testbench’s proportional-integral-derivative (PID), synchronous proportional-integral-derivative (SPID), and SMC controllers.

UNIVERSAL STRUCTURAL SYSTEM OF CLOSED KINEMATIC CHAINS OF MOVABLE LINKS AND ITS APPLICATION FOR THE SYNTHESIS OF STRUCTURAL SCHEMES OF THESE CHAINS

The article shows the possibility of developing the method of structural synthesis of flat closed kinematic chains by M. Grubler, into closed kinematic chains of moving links of all families and spaces. The universal structural system of Professor L. T. Dvornikov for closed kinematic chains of moving links of all families and spaces is given. A complete set of solutions has been found describing the organization of closed kinematic chains of movable links of the second, third and fourth subfamilies of the first family with the complexity of the basic chain link equal to two and three, the mobility of the chain equal to six and the total number of chain links from three to six. Combinations of kinematic pairs and links have been obtained, which make it possible to find all, without exception, structural schemes closed kinematic chains of movable links of the first family under given parameters, from which, by stopping a link connected to an adjacent link of the chain by a kinematic pair of the fifth class, single-moving assur mechanisms can be formed.

Biomechanical Aspects regarding Restoration of Shoulder Stability in Athletes

Although the recovery of the body after exertion or post-trauma is particularly important, in contemporary sports, for various reasons, it is often not given the necessary time. The main objective of the research was to study the biomechanical particularities of the shoulder that ensure mobility and stability in order to recover post-luxation. The research activity was carried out on two athletes, during 8 months, and we followed the restoration of muscle imbalances and the biomechanical analysis of the unstable shoulder. The objectives of the research were to select the most effective methods and means of physical therapy, by which to restore the stability of the post-luxation shoulder, in athletes. As working methods we used exercises performed in a closed kinematic chain and neuromuscular and proprioceptive facilitation techniques, balancing the forces of the deep muscles. In conclusion, it can be said that through isometric work in a closed kinematic chain and through neuromuscular and proprioceptive facilitation techniques, we can balance the stabilizing muscle forces at the level of the shoulder joint. Through the recovery sessions performed, the muscle imbalances were diminished by the considerable increase in the muscle strength of the per articular muscles.

СТРУКТУРНЫЙ СИНТЕЗ ЗАМКНУТЫХ КИНЕМАТИЧЕСКИХ ЦЕПЕЙ ПОДВИЖНЫХ ЗВЕНЬЕВ ПЯТОГО, ШЕСТОГО, СЕДЬМОГО И ВОСЬМОГО ПОДСЕМЕЙСТВ ПЕРВОГО СЕМЕЙСТВА

The study objective is to develop a method of structural synthesis of closed kinematic chains of moving links into the fifth, sixth, seventh and eighth subfamilies of the first family.
 Tasks: to obtain a complete set of solutions describing the arrangement of closed kinematic chains of moving links of the fifth, sixth, seventh and eighth subfamilies of the first family with the complexity of the basic chain link equal to two and three, the mobility of the chain equaling to six and the total number of chain links from 3 to 6 based on the universal structural system of Professor L.T. Dvornikov for closed kinematic chains of moving links of the first family. Using the data obtained, consider the construction of a block diagram of a closed kinematic chain of moving links of the first family on a specific example.
 Research methods: a method of structural synthesis of closed kinematic chains of moving links of the first family is used.
 The novelty of the work: the peculiarities of applying a universal structural system for determining the composition of closed kinematic chains of moving links of the fifth, sixth, seventh and eighth subfamilies of the first family are considered. An example of using the obtained combinations of kinematic pairs and links for the synthesis of structural schemes of closed kinematic chains of moving links of the first family is shown.
 Study results: combinations of kinematic pairs and links are obtained, which make it possible to find structural schemes of closed kinematic chains of moving links of the fifth, sixth, seventh and eighth subfamilies of the first family under given parameters, from which single-moving mechanisms of the first family can be formed by stopping the link.

Study of Differential Evolution Variants in the Dimensional Synthesis of Four-Bar Grashof-Type Mechanisms

Mechanisms have allowed for the automation of complex, repetitive, demanding, or dangerous tasks for humans. Among the different mechanisms, those with a closed kinematic chain are more precise and robust compared to open chain ones, which makes them suitable for many applications. One of the most widely used closed-chain alternatives is the four-bar Grashof-type mechanism, as it can generate highly nonlinear closed trajectories with a single degree of freedom. However, the dimensional synthesis of these mechanisms to generate specific trajectories is a complex task. Fortunately, computational methods known as metaheuristics can solve such problems effectively. Differential Evolution (DE) is a metaheuristic commonly used to tackle the dimensional synthesis problem. This paper presents a comparative study of the most commonly used variants of DE in solving the dimensional synthesis problem of four-bar Grashof-type mechanisms. The purpose of the study is to provide guidelines to choose the best DE alternative for solving problems of this type, as well as to support the development of DE-based algorithms that can solve more specific cases effectively. After analysis, the rand/1/exp variant was found to be the most effective in solving the dimensional synthesis problem, which was followed by best/1/bin. Based on these results, a Simple and Improved DE (SIDE) variant based on these two was proposed. The competitive performance of the SIDE with respect to the studied DE variants and in contrast to the results of algorithms used in the recent specialized literature for mechanism synthesis illustrates the usefulness of the study.

Modeling, Cooperative Planning and Compliant Control of Multi-arm Space Continuous Robot for Target Manipulation

In this paper, a modeling, cooperative planning and compliant control method is presented for multi-arm space continuous robots in target manipulation. Firstly, according to the closed-chain relationship between the multi-arm space continuous robot and the target, the general equations of the closed-chain kinematics and the closed-chain dynamics are derived. Secondly, according to the above mathematical equations, the trajectory planning model of multi-arm space continuous robots for pre-capture and post-capture is established. For the pre-capture process, the null space is used to search out the cable length parameters under the limited joint angle. For the post-capture process, the nonlinear optimization method is used to find the solution that minimizes the disturbance of the base. Thirdly, aiming at the problem of internal force distribution and pose control after target capture, a compliant control model of multi-arm space continuous robots for target manipulation is constructed, so as to minimize the cable tension in the process of force/pose hybrid control. Finally, the proposed method is verified based on the Matlab/Simechanics co-simulation model. The simulation results prove the effectiveness of the proposed method.

Effectiveness of Pilates Exercises versus Closed Kinematic Chain Exercises in Knee Osteoarthritis Post - Menopausal Women - An Experimental Study

Effectiveness of Pilates Exercises versus Closed Kinematic Chain Exercises in Knee Osteoarthritis Post - Menopausal Women - An Experimental Study

Two-Dimensional Mechanical Model of Human Stability in External Force-Caused Fall

The paper proposes a two-dimensional model of human stability. The model allows for gaining data on forces and moments of forces being the effect of musculoskeletal interactions of body parts at human joints. The necessary input data are registered with the use of an optoelectronic motion capture system, two force plates, and a dynamometer. The latter measures the magnitude of the external force that is randomly applied to cause a backward fall. Therefore, the position of the participant’s body during the experiment, the external force used to cause the fall, and the ground reaction forces are known. The model proposed has the structure of a closed kinematic chain with one loop and two open subchains and uses the Euler–Newton approach to analyse the motion. In addition to external loads, linear and angular accelerations are also needed. To calculate those, we used a variant of approximation. This consists in carrying out a simultaneous approximation of a given function and its first and second derivatives in the subintervals that shift along the whole data range. The experiments conducted include two activities while maintaining a state of equilibrium and the fall itself. This gives the basis for examining whether the internal forces and moments at human joints differ significantly in both these states. The results and conclusions are discussed in the final part of the paper.

Kinetostatic Optimization for Kinematic Redundancy Planning of Nimbl’Bot Robot

AbstractIn manufacturing industry, computer numerical control (CNC) machines are often preferred over industrial serial robots (ISR) for machining tasks. Indeed, CNC machines offer high positioning accuracy, which leads to slight dimensional deviation on the final product. However, these machines have a restricted workspace generating limitations in the machining work. Conversely, ISR are typically characterized by a larger workspace. ISR have already shown satisfactory performance in tasks like polishing, grinding, and deburring. This paper proposes a kinematic redundant robot composed of a novel two degrees-of-freedom mechanism with a closed kinematic chain. After describing a task-priority inverse kinematic control framework used for joint trajectory planning exploiting the robot kinematic redundancy, the paper analyses the kinetostatic performance of this robot depending on the considered control tasks. Moreover, two kinetostatic tasks are introduced and employed to improve the robot performance. Simulation results show how the robot better performs when the optimization tasks are active.

Petri nets-based digital twin drives dual-arm cooperative manipulation

The emerging concept of digital twin (DT) creates a holistic vision to change how we view the design and operation of a cyber-physical system (CPS), and how to reconfigure its function and structure to deal with the scenario of complexity and uncertainty that arises from reality. In this work, we firstly surveyed the typical narrative frameworks of DT modelling: generalized layered method, decomposition and composition method, Asset Administration Shell framework, and standardized architecture. Secondly, the Petri nets-based digital twin framework for the robotic dual-arm cooperative system was presented in detail through the domain-based and entity-based systematization methodology. The proposed framework generated a conceptually embodied and situated DT environment, which not only represented the highly hybrid nature (i.e., continuous, discrete and cooperative) of the dual-arm cooperative operation process, but also avoided the complex decoupling calculation of closed kinematic chains in the bi-manual manipulation of industrial arms. Furthermore, two digital twin instances clearly demonstrated that the holonic integration of operational technologies equipment, information technologies and DT through the industrial internet of things manifested a game-changing potential to upgrade the capability of an existing brownfield CPS to perform complex tasks. Concluding, by coupling the discrete event simulation at the highly abstract level and the 3D offline programming simulation in the intuitively DT environment, this comprehensive practice of DT to transform the loose DT metaphor into strictly industrial domains provided an illuminating cross-increment for both the robotic community and the DT facilitators.