Closed-chain Mechanism Research Articles

Assessment of Kinematic and Dynamic Characteristics of Shoulder Mechanism

Introduction: The thorax, clavicula, scapula and humerus comprise the finite element musculoskeletal model of the shoulder mechanism, which has been used to analyse its kinematic and dynamic behaviour. The study aims to reflect upon the analysis of the kinematic and dynamic behaviour of the shoulder mechanism. Materials and Methods: A comprehensive literature search was conducted to identify the relevant literature. Databases such as PubMed, Scopus and Google Scholar were used to search for literature published between 2000 and 2023. Results: The scapulothoracic gliding plane’s motion restrictions, which convert the shoulder girdle into a closed-chain mechanism, are represented in the model along with 16 muscles, 3 joints and 3 extracapsular ligaments. The locations of the humerus and shoulder girdle that were recorded in ten subjects during loaded and unloaded humeral abduction and anteflexion are the input variables. Conclusion: The length dependence of electromyography (EMG) amplitude and the unknown force-length relationship makes it difficult to compare muscle force predictions and EMG measurements. The conclusion is that complicated musculoskeletal models cannot be validated using EMG amplitude. The force and moment balance of the three joints are used to examine the function of the muscles. This model allows for an investigation of the function of morphological components and offers useful insight into the mechanics of the shoulder mechanism.

Design and research of a new multi-loop closed-chain morphing wing mechanism

Innovative design and investigation into multi-configurable morphing wing mechanism (MWM) have been focused on meeting the evolving needs of morphing aircraft with extensive spatial and velocity domains. In this paper, a design methodology for multi-loop closed-chain mechanism (MLCCM) involved the substitution of Bennett mechanism links with sub-mechanisms, and an innovative design of 4-RSPCR MLCCM is proposed based on the method, incorporating equivalent spherical mechanism and group theory. Subsequently, a multi-module morphing wing mechanical network consisting of the 4-RSPCR MLCCM is proposed, and the degrees of freedom (DOF) for the multi-module MWM is analyzed using graph theory. In addition, kinematic models for single module mechanism are established, and research on kinematic modeling methods for multi-module mechanisms is conducted. Finally, a prototype of a six-module MWM is constructed, and deformation experiments is conducted. The results show that the proposed innovative mechanisms and the novel multi-module morphing wing mechanical network facilitate the serialized design for various wing planar shapes. Furthermore, these mechanisms enable multi-configurational deformations, including bi-directional bending and variable span. These findings lay the groundwork for fundamental research and engineering applications of morphing wings in morphing aircraft.

A Novel Explicit Canonical Dynamic Modeling Method for Multi-Rigid-Body Mechanisms Considering Joint Friction

Friction is an inevitable phenomenon in mechanical systems that affects the dynamic characteristics of systems. To reduce the modeling complexity of complex multi-rigid-body mechanisms, a novel explicit canonical dynamic modeling method considering joint friction is proposed. Based on the explicit dynamic modeling theory that we have proposed, the solution of the constraint force required by the joint friction modeling of multi-rigid-body mechanisms is derived and improved, which greatly simplifies the solution of the constraint force. According to the obtained explicit expression of the constraint force equations, two joint friction models of the Coulomb–viscous effect and Stribeck effect are derived in analytical form. Moreover, the Stribeck effect of the joint is experimentally analyzed. A five-axis tree-chain mechanism and a three-loop closed-chain mechanism are chosen to demonstrate the method and compared with ADAMS software. Moreover, the proposed model is analyzed and compared with other methods.

Design optimization and testing of a morphing leading-edge with a variable-thickness compliant skin and a closed-chain mechanism

Climate warming and the increased demand in air travels motivate the aviation industry to urgently produce technological innovations. One of the most promising innovations is based on the smoothly continuous morphing leading-edge concept. This study proposes a two-step process for the design of a morphing leading-edge, including the optimization of the outer variable-thickness composite compliant skin and the optimization of the inner kinematic mechanism. For the compliant skin design, an optimization of the variable thickness composite skin is proposed based on a laminate continuity model, with laminate continuity constraint and other manufacturing constraints. The laminate continuity model utilizes a guiding sequence and a ply-drop sequence to describe the overall stacking sequence of plies in different thickness regions of the complaint skin. For the inner kinematic mechanism design, a coupled four-bar linkage system is proposed and optimized to produce specific trajectories at the actuation points on the stringer hats of the compliant skin, which ensures that the compliant skin can be deflected into the aerodynamically optimal profile. Finally, a morphing leading-edge is manufactured and tested. Experimental results are compared with numerical predictions, confirming the feasibility of the morphing leading-edge concept and the overall proposed design approach.

An innovative joint-space explicit dynamics symbolic computation model for closed-chain mechanisms

In this article, an innovative joint-space explicit dynamics symbolic computation model for closed-chain mechanisms is proposed, which greatly reduces the symbolic and numerical complexity. This study is developed based on our previous work on the explicit dynamics model of tree-chain. The closed-chain mechanism problem is decoupled into a tree-chain problem by using the method of simplified system dynamics, and then the kinematic constraint equation and constraint force equation of the closed-chain are derived based on Axis-Invariant, which greatly simplifies the establishment and solution of the kinematic constraint equation and constraint force vector. The correctness and universality of the proposed method are verified by two common closed-chain mechanisms by comparison using ADAMS software. The advantage of the proposed method lies in the fact that the modeling and solution complexity can be greatly reduced, which is analyzed by comparison with Stefan Staicu's method.

Neuronal Constraint-Handling Technique for the Optimal Synthesis of Closed-Chain Mechanisms in Lower Limb Rehabilitation

The optimal methods for the synthesis of mechanisms in rehabilitation usually require solving constrained optimization problems. Metaheuristic algorithms are frequently used to solve these problems with the inclusion of Constraint-Handling Techniques (CHTs). Nevertheless, the most used CHTs in the synthesis of mechanisms, such as penalty function and feasibility rules, generally prioritize the search for feasible regions over the minimization of the objective function, and it notably influences the exploration and exploitation of the algorithm such that it could induce in the premature convergence to the local minimum and thus the solution quality could deteriorate. In this work, a Neuronal Constraint-Handling (NCH) technique is proposed and its performance is studied in the solution of mechanism synthesis for rehabilitation. The NCH technique uses a neural network to search for the fittest solutions into the feasible and the infeasible region to pass them to the next generation of the evolutionary process of the Differential Evolution (DE) algorithm and consequently improve the obtained solution quality. Two synthesis problems with four–bar and cam–linkage mechanisms are the study cases for developing lower-limb rehabilitation routines. The NCH is compared with four state-of-the-art constraint-handling techniques (penalty function, feasibility rules, stochastic ranking, ϵ-constrained method) included into four representative metaheuristic algorithms. The irace package is used for both the algorithm settings and neuronal network training to fairly and meaningfully compare through statistics to confirm the overall performance. The statistical results confirm that, despite changes in the rehabilitation trajectories, the proposal presents the best overall performance among selected algorithms in the studied synthesis problems for rehabilitation, followed by penalty function and feasibility rule.

Adaptive proportional-integral-derivative control for surgical plane cable-driven robots

Robotic technology has greatly improved the success rate of the surgeries by transmitting complicated operations from the surgeon to the tool. In this way, cable-driven robots operate in narrow spaces and take high loads with low weights and costs. This research work presents an adaptive Proportional-Integral-Derivative (PID) controller for surgical plane cable-driven robots and optimizes the gains by employing a Particle Swarm Optimization (PSO) approach. In this way, the general equation of kinematics and dynamics of the robot are investigated regarding a closed chain mechanism and the actuators adjoined to the base. An adaptive PID controller based on the robust sliding surfaces and gradient descent rules is applied to handle the end-effector (tool) to different desired conditions. The proper values of the control gains are found by using the PSO algorithm as a swarm-based technique for minimizing the output errors. The simulation results clearly indicate the capability of the introduced control approach to tracking the constant and time-dependent desired trajectories in the presence of external disturbances.

The Kinematic and Dynamic Modeling and Numerical Calculation of Robots with Complex Mechanisms Based on Lie Group Theory

The kinematic and dynamic models of robots with complex mechanisms such as the closed-chain mechanism and the branch mechanism are often very complex and difficult to be calculated. Aiming at this issue, in this paper, the pose of the component in robots is represented by the Euclidean group and its subgroups with the proposed method. The component’s velocity is derived using the relationship between the Lie group and Lie algebra, and the acceleration and Jacobian matrix are then derived on this basis. The Lagrange equation is expressed by the obtained kinematic parameter expressions. Establishing the model with this method can obtain clear physical meaning and make the expressions uniform and easy to program, which is convenient for computer-aided calculation and parameterization. Calculating by the properties of the Lie group can reduce the calculation and model complexity, especially for calculating the velocity and acceleration, which reduces the calculation error and eases the calculation. Therefore, the proposed modeling and calculation method of kinematics and dynamics of robots is especially suitable for robots with complex mechanisms. As an example, the kinematic and dynamic model of the manipulator developed in our laboratory is established and a working process of it is numerically calculated. Then, the results of the numerical calculation are compared with the results of virtual prototype simulation in ADAMS to verify the correctness.

Design and evaluation of a novel upper limb rehabilitation robot with space training based on an end effector

Abstract. The target of this paper is to design a lightweight upper limb rehabilitation robot with space training based on end-effector configuration and to evaluate the performance of the proposed mechanism. In order to implement this purpose, an equivalent mechanism to the human being upper limb is proposed before the design. Then, a 4 degrees of freedom (DOF) end-effector-based upper limb rehabilitation robot configuration is designed to help stroke patients perform space rehabilitation training of the shoulder flexion/extension and adduction/abduction and elbow flexion/extension. Thereafter, its kinematical model is established together with the proposed equivalent upper limb mechanism. The Monte Carlo method is employed to establish their workspace. The results show that the overlap of the workspace between the proposed mechanism and the equivalent mechanism is 96.61 %. In addition, this paper also constructs a human–machine closed-chain mechanism to analyze the flexibility of the mechanism. According to the relative manipulability and manipulability ellipsoid, the highly flexible area of the mechanism accounts for 67.6 %, and the mechanism is far away from the singularity on the drinking trajectory. In the end, the single-joint training experiments and a drinking water training trajectory planning experiment are developed and the prototype is manufactured to verify it.

Development and Analysis of a Closed-Chain Wheel-Leg Mobile Platform

Current research concerning legged platforms and wheeled platforms primarily focuses on terrain adaptive capability and speed capability, respectively. Compared with wheeled platforms, legged platforms with a closed-chain mechanism still present deficiencies regarding speed ability. To integrate the advantages of these two types of platforms, a wheel-leg mobile platform with two modes based on a closed-chain mechanism is proposed. First, a closed-chain mechanism that generates a high-knee trajectory in legged mode is designed and analyzed based on kinematic analysis. To improve the platform’s obstacle-surmounting performance, the dimensional parameters of the closed-chain mechanism are optimized and the design requirements for the platform’s frame are analyzed. In addition, the particular structure of the leg group is designed to realize transformation between legged mode and wheeled mode. The mobility of the constructed platform is calculated through an obstacle-surmounting probability analysis. The performances of the two motion modes are analyzed and compared by conducting dynamic simulations. Finally, experiments are carried out to verify both the theoretical analyses and the prototype performance. This study proposes a new approach to designing wheel-leg platforms with prominent speed ability and mobility based on a closed-chain mechanism.

Design and analysis of a novel octopod platform with a reconfigurable trunk

In order to enhance the terrain mobility of the close-chain leg mechanism and maximize its advantages, a novel dual degree-of-freedom (DoF) octopod platform with a reconfigurable trunk is proposed. The walking strategy of the close-chain multi-legged mechanism is adjusted through the spatial close-chain trunk mechanism. These two single-DoF close-chain mechanisms are designed and coupled to constitute whole close-chain mechanism as the walking platform. The locomotion modes of the trunk are discussed with the mobility analysis. In steering mode, the motion characteristic is analyzed under the combined action of steering linkage and elastic deformation. In climbing mode, the kinematic analysis and dimensional optimization are carried out, and the obstacle-climbing ability is evaluated through the probability model. To enhance climbing smoothness and efficiency, the assisted appendage is developed with the inner loop of Watt-Ⅰ leg linkage. A series of dynamic simulations is conducted and analyzed to test the platform performance, and a prototype is fabricated to testify the walking speed, steering property and obstacle-climbing capability. This study provides a new reference for close-chain legged platform development.

Kinematic Analysis of the Robot Having Closed Chain Mechanisms Based on an Improved Modeling Method and Lie Group Theory

The robot kinematic model is the basis of motion control, calibration, error analysis, etc. Considering these factors, the kinematic model needs to meet the requirements of completeness, model continuity, and minimality. DH model as the most widely used method to build robot kinematic model still has problems in completeness, model continuity, and calculation, especially for robots with complex mechanisms such as closed chain mechanism and branch mechanism. In this paper, an improved kinematic modeling method is proposed based on the cooperation of the DH model and the Hayati and Mirmirani model and considering the Lie group concept. The improved model is complete and continuous, and when combining with Lie group to calculate, it avoids numbers of trigonometric functions and antitrigonometric functions in the process so as to optimize the algorithm. With this method, the kinematic model of the closed chain cascade manipulator developed in our laboratory is established, and a working process of it is numerically calculated. The results of the numerical calculation are basically consistent with those of virtual prototype simulation, which means the established kinematic model is correct and the numerical calculation method can solve the problem correctly. The kinematic model and the results of the kinematic analysis provide a theoretical basis for the subsequent motion control, calibration, and error analysis of the robot.

Visual Closed-Loop Dynamic Model Identification of Parallel Robots Based on Optical CMM Sensor

Parallel robots present outstanding advantages compared with their serial counterparts; they have both a higher force-to-weight ratio and better stiffness. However, the existence of closed-chain mechanism yields difficulties in designing control system for practical applications, due to its highly coupled dynamics. This paper focuses on the dynamic model identification of the 6-DOF parallel robots for advanced model-based visual servoing control design purposes. A visual closed-loop output-error identification method based on an optical coordinate-measuring-machine (CMM) sensor for parallel robots is proposed. The main advantage, compared with the conventional identification method, is that the joint torque measurement and the exact knowledge of the built-in robot controllers are not needed. The time-consuming forward kinematics calculation, which is employed in the conventional identification method of the parallel robot, can be avoided due to the adoption of optical CMM sensor for real time pose estimation. A case study on a 6-DOF RSS parallel robot is carried out in this paper. The dynamic model of the parallel robot is derived based on the virtual work principle, and the built dynamic model is verified through Matlab/SimMechanics. By using an outer loop visual servoing controller to stabilize both the parallel robot and the simulated model, a visual closed-loop output-error identification method is proposed and the model parameters are identified by using a nonlinear optimization technique. The effectiveness of the proposed identification algorithm is validated by experimental tests.

Design and Analysis of a Sixteen-Legged Vehicle With Reconfigurable Close-Chain Leg Mechanisms

In order to exert the advantages of simplified control and integral rigidity, a novel 16-legged walking vehicle is proposed as a carrying platform based on closed-chain mechanisms. Considering the demand for mobility of one degree-of-freedom leg mechanism, we adopt the reconfigurable approach for trajectory flexibility. Serving as a walking module, the whole close-chain leg mechanism is designed to construct the walking vehicle. On the basis of kinematic analysis and sensitivity analysis, the reconfigurable leg with “gluteus maximus” is presented for increasing the obstacle-surmounting ability. In terms of the whole vehicle, the reconfiguration assignments and strategies are analyzed to satisfy the different climbing requirements. The obstacle-climbing capabilities of the legged units are evaluated through the probability analysis. In slope-climbing process, the supporting and the propelling regions for reconfiguration are discussed and obtained with two decision conditions. A series of dynamic simulations and experiments are performed to testify the walking stability, the walking speed, the steering performance, the terrain adaptability, and the obstacle-surmounting capability.

Closed-Loop Position and Cadence Tracking Control for FES-Cycling Exploiting Pedal Force Direction With Antagonistic Biarticular Muscles

A functional electrical stimulation (FES)-based position and cadence tracking controller is developed to enable cycling by exploiting antagonistic biarticular muscles. A model of a stationary cycle and a rider is developed as a closed-chain mechanism. A strategy is then developed to switch between muscle groups based on the force direction of each muscle group. Stability of the developed controller is analyzed through Lyapunov-based methods. Experiments were conducted in seven healthy individuals and one individual with Parkinson’s disease to illustrate the performance of the developed method. Specifically, the developed method was compared with voluntary tracking in terms of the position and velocity tracking errors. From the experimental results, we conclude that the proposed method can realize FES-cycling close to voluntary tracking.

Design and analysis of a novel walking vehicle based on leg mechanism with variable topologies

In order to improve the adaptability of one-degree-of-freedom leg mechanism to unknown terrains while maintaining its control simplicity, energy efficiency and integral rigidity, a novel close-chain mechanism with variable topological structures is proposed to act as a single leg to generate different gaits. The design process of the closed kinematic chain is completed by integrating two types of mechanical joints. Besides, the kinematics of the single leg under two modes is analyzed using vector loop method, and the particular structure of the leg mechanism is designed with optimized parameters. The topological states are represented with graphs and a matrix. Moreover, the whole close-chain legged unit and the walking vehicle are developed and constructed. In particular, to evaluate the crossing ability, this paper proposes the obstacle-surmounting probability. A series of dynamic walking simulations is conducted and analyzed to support the obstacle-surmounting capability and mobility comparison. Legged units are fabricated to verify the theoretical analysis, and walking experiments with a multi-legged vehicle are performed to testify the prototype performance.

Dual-arm cooperative manipulation under joint limit constraints

Abstract Cooperative manipulation of a rigid object is challenging and represents an interesting and active research area, especially when these robots are subject to joint and task prioritization constraints. In cooperative manipulation, a primary task is to maintain the coordination of motions, to avoid severe damage caused by the violation of kinematic constraints imposed by the closed chain mechanism. This paper proposes a kinematic controller for dual-arm cooperative manipulation that ensures safety by providing relative coordinated motion as highest priority task and joint limit avoidance and world-space trajectory following at a lower priority. The coordination of motions is based on modular relative Jacobian formulation. The approach is applicable to systems composed of redundant or non-redundant manipulators. Experiments in simulation demonstrate the behavior of the approach under different redundancy configurations. Experiments on two robots with different number of redundant motions show the applicability of the proposed approach to cooperative manipulation under joint limit constraints.

Design and analysis of a novel multi-legged horse-riding simulation vehicle for equine-assisted therapy

A novel multi-legged horse-riding simulation vehicle aiming at providing the equine-assisted therapy is proposed, the functions of which include both transportation and rehabilitation. The whole system consists of a walking system constructed with four identical-legged units, a control system, an energy system, and a riding system. Based on the requirements of the foot trajectory, the configuration of the whole close-chain legged mechanism serving as a legged unit is designed with the structure of a single leg. The kinematics of the legged mechanism is built using the vector loop method, and the dimension is optimized adopting the sequence quadratic program. With the established mathematic model, the form-position inversion method is developed for the fluctuation analysis of the riding platform, and its modified algorithm is proposed according to the walking properties. The closed fluctuating curve group is obtained when the riding platform walks on a treadmill with a constant speed, and two functional curves are selected and analyzed for different walking modes. Combined with the practical requirements of different intensities, the sensitivity analysis is carried out for the reconfigurable process to adjust the fluctuation amplitude. A series of dynamic walking simulations are conducted and analyzed, and a prototype is fabricated to verify the expected functions of the multi-legged riding simulation vehicle. The study provides a new idea and an application reference for equine-assisted therapy system.

다축 동기 제어 방법 기반의 산업용 고속 병렬로봇 제어

Parallel robots are usually used for performing pick-and-place motion to increase productivity in high-speed environments. The present study proposes a high-speed parallel robot and a control approach to improve the tracking performance for the purpose of handling a solar cell. However, the target processes are not limited to the solar cell-handling field. Therefore, a delta-type parallel manipulator is designed, and a ball joint structure is specifically proposed to increase the allowed angle that would meet the required workspace. A control algorithm considering the synchronization between multiple joints in a closed-chain mechanism is also suggested to improve the tracking performance, where the tracking and synchronization errors are simultaneously considered. In addition, a prototype machine with the proposed ball joint is implemented. A satisfactory tracking performance is achieved by applying the proposed control algorithm, with a cycle time of 0.3 s for a 0.1 kg payload.

Differential Flatness Theory-Based Adaptive Fuzzy Control of Underactuated Nonlinear Systems

An adaptive fuzzy controller is designed for a class of underactuated nonlinear robotic manipulators, under the constraint that the system’s model is unknown. The control algorithm aims at satisfying the $$H_\infty $$ tracking performance criterion, which means that the influence of the modeling errors and the external disturbances on the tracking error is attenuated to an arbitrary desirable level. After transforming the robotic system into the canonical form, the resulting control inputs are shown to contain nonlinear elements which depend on the system’s parameters. The nonlinear terms which appear in the control inputs are approximated with the use of neuro-fuzzy networks. It is shown that a suitable learning law can be defined for the aforementioned neuro-fuzzy approximators so as to preserve the closed-loop system stability. With the use of Lyapunov stability analysis it is proven that the proposed adaptive fuzzy control scheme results in $$H_{\infty }$$ tracking performance. The efficiency of the proposed adaptive fuzzy control scheme is checked in the case of a 2-DOF planar robotic manipulator that has the structure of a closed-chain mechanism.