Closed Kinematic Chains Research Articles

Real-Time Trajectory Generation Methods for Cooperating Mobile Manipulators Subject to State and Control Constraints

This paper deals with the real-time trajectory generation problem for two cooperating mobile robots moving the common rigid object. The holonomic constraints resulting from a closed kinematic chain and the dynamics of such a system are considered. Two methods of generation sub-optimal trajectories allowing for mechanical and control limitations and collision avoidance conditions are proposed. The first solution is based on a leader-follower approach, in the second one the robotic system is treated as a whole mechanism. In both cases, the trajectories are generated in order to avoid singularities and they are scaled to satisfy control constraints. Advantages and disadvantages of both presented approaches are discussed. A computer example involving two mobile manipulators consisting of nonholonomic platform (2,0) class and planar 3-DOF holonomic manipulator is presented.

Reliability of Axial-Thoracolumbar Spine Rotation Range Measurements

Background Although numerous measurement methods exist for thoracolumbar spine rotation, achieving an accurate measurement of axial-thoracolumbar spine rotation is difficult because it is usually measured in the open kinematic chain. Purpose Therefore, the purpose of our study was to investigate the reliability of a new method for measuring axial-thoracolumbar spine rotation in the closed kinematic chain. Study design Intra-tester repeated measures Methods 14 healthy participants performed axial-thoracolumbar rotation. An electromagnetic tracking system was used to measure the angle of axial-thoracolumbar rotation in the sternum’s jugular notch and xiphoid process. Results The test-retest reliability of the axial-thoracolumbar rotation angle per the sensor on the jugular notch was 0.83, and the measurement from the sensor on the xiphoid process was 0.84. Conclusions The measurement of the axial-thoracolumbar rotation angle in the supine position showed excellent reliability.

Features Geometric Analysis of Planar Mechanisms

The current paper focuses on one of the units of the TMM course and continues a series of the published works. In previous publications we discussed the questions of the generation and solution of the equations of geometric analysis. It was shown that equations of geometric analysis composed for closed kinematic chains are trigonometric or algebraic nonlinear equations. If they possess a solution then it is not a unique one, as a rule. Several solutions of the set of geometric equations mean that at given input coordinates and a predetermined position of fixed hinged joints the mechanism could be put together in several ways. In other words, some configuration diagrams of the mechanism exist. Configuration diagrams which cannot be used without their dissembling are called the assemblies of the mechanism.

Symbolic Geometric Modelling of Tree‐Structure Robotic Mechanisms Using Lie Groups and Graph Theory

AbstractThe present work describes a symbolic formulation based on Lie groups and graph theory to obtain the dynamic equations of tree‐structure robotic mechanisms (TRM)s. The resulting equation is the equivalent geometric form of the classical Newton‐Euler's equation of motion. Such formulation is valid for any TRM without closed kinematic chains and whose joints have one degree of freedom (revolute and/or prismatic). For instance, open chain manipulator, robotic hands or humanoids are included within TRM. The structure of the proposed formulation allows analytic differentiation, which is required for techniques such as optimal control or robust control. Moreover, the assembly parameters are explicitly held in matrices, so that they can be mathematically manipulated in order to be adapted for simulation, analysis or identification algorithms. Finally, the formulation is applied to a 7DOF manipulator and to a two arm torso of 16 degrees of freedom. The results are compared with the multi‐body simulation software package MSC/ADAMS© proving the correctness of the formulation.

Closed-Chain Manipulation of Large Objects by Multi-Arm Robotic Systems

Closed kinematic chains are created whenever multiple robot arms concurrently manipulate a single object. The closed-chain constraint, when coupled with robot joint limits, dramatically changes the connectivity of the configuration space. We propose a regrasping move, termed "IK-switch", which allows efficiently bridging components of the configuration space that are otherwise mutually disconnected. This move, combined with several other developments, such as a method to stabilize the manipulated object using the environment, a new tree structure, and a compliant control scheme, enables us to address complex closed-chain manipulation tasks, such as flipping a chair frame, which is otherwise impossible to realize using existing multi-arm planning methods.

Adaptive hybrid position/force control of dual-arm cooperative manipulators with uncertain dynamics and closed-chain kinematics

In this paper, a novel adaptive control for dual-arm cooperative manipulators is proposed to accomplish the hybrid position/force tracking in the presence of dynamic and closed-chain kinematic uncertainties. Self-convergent parameter estimation of the grasped object's centre of mass and contact force estimation are incorporated into this systematic scheme. Moreover, internal force and contact force tracking objectives are achieved simultaneously by incorporating into the position tracking formula with proper null-space projection and rotation transformation. Noisy force derivative signals are not required. This adaptive controller is mathematically derived based on Lyapunov stability analysis. Three sets of simulations corresponding to three different situations are presented to verify the effectiveness and superiority of the proposed controller.

Fuzzy Model Based Stability Analysis of the Metamorphic Robotic Palm

The metamorphic hand can flexibly relocate fingers by a reconfigurable palm. A precondition for the successful hand operation would be a stable palm control system. Following this concern, this paper presents the stability analysis of the reconfigurable palm control system based on the Takagi-Sugeno (T-S) fuzzy model. The dynamic model of the metamorphic palm is developed by using the Euler Lagrangian theory and the closed-chain kinematic constraints. To further reduce the conservativeness in stability analysis and ensure a wider range of stable dynamic performance, a membership-dependent fuzzy modeling approach is also applied. Simulation is provided to demonstrate the achieved improvement of analysis results.

Active Rehabilitation Exercises With a Parallel Structure Ankle Rehabilitation Prototype

In this paper the implementation of impedance controllers to develop active rehabilitation exercises are presented. For which it is used a parallel structure ankle rehabilitation prototype with a mechanism of the type 2-RRSP (two closed kinematic chains and consisting of joints: revolute-revolute-sphere in slot- fixed post with sphere). Free software is used to develop the computer programs associated with rehabilitation exercises. The results of active rehabilitation exercises are reported, wich involves the effect of resistance from the rehabilitation prototype to the user operation: low, medium and high opposition effects are considered.

Adaptive neural network visual servoing of dual-arm robot for cyclic motion

PurposeThe purpose of this paper is to develop a vision-based dual-arm cyclic motion method, focusing on solving the problems of an uncertain grasp position of the object and the dual-arm joint-angle-drift phenomenon.Design/methodology/approachA novel cascade control structure is proposed which associates an adaptive neural network with kinematics redundancy optimization. A radial basis function (RBF) neural network in conjunction with a conventional proportional–integral (PI) controller is applied to compensate for the uncertainty of the image Jacobian matrix which includes the estimated grasp position. To avoid the joint-angle-drift phenomenon, a dual neural network (DNN) solver in conjunction with a PI controller and dual-arm-coordinated constraints is applied to optimize the closed-chain kinematics redundancy.FindingsThe proposed method was implemented on an industrial robotic MOTOMAN with two 7-degrees of freedom robotic arms. Two experiments of carrying a tray repeatedly and turning a steering wheel were carried out, and the results indicate that the closed-trajectories tracking is achieved successfully both in the image plane and the joint spaces with the uncertain grasp position, which validates the accuracy and realizability of the proposed PI-RBF-DNN control strategy.Originality/valueThe adaptive neural network visual servoing method is applied to the dual-arm cyclic motion with the uncertain grasp position of the object. The proposed method enhances the environmental adaptability of a dual-arm robot in a practical manipulation task.

The significance of closed kinematic chains to biological movement and dynamic stability

Closed kinematic chains (CKCs) are widely used in mechanical engineering because they provide a simple and efficient mechanism with multiple applications, but they are much less appreciated in living tissues. Biomechanical research has been dominated by the use of lever models and their kinematic analysis, which has largely ignored the geometric organization of these ubiquitous and evolutionary-conserved systems, yet CKCs contribute substantially to our understanding of biological motion.Closed-chain kinematics couple multiple parts into continuous mechanical loops that allow the structure itself to regulate complex movements, and are described in a wide variety of different organisms, including humans. In a biological context, CKCs are modular units nested within others at multiple size scales as part of an integrated movement system that extends throughout the organism and can act in synergy with the nervous system, where present. They provide an energy-efficient mechanism that enables multiple mechanical functions to be optimized during embryological development and increases evolutionary diversity.

The Association of Forefoot Varus Deformity with Patellofemoral Cartilage Damage in Older Adult Cadavers

Forefoot alignment may contribute to patellofemoral joint (PFJ) osteoarthritis (OA) via its influence on the closed chain kinematics of the lower limb. The purpose of this cadaveric study was to investigate the relationship between forefoot varus and ipsilateral cartilage damage in the medial and lateral PFJ. Forefoot alignment measurements were obtained from the feet of 25 cadavers (n = 50). Cartilage damage in the medial and lateral PFJ of each knee was scored using the Outerbridge scale. The relative odds of medial and lateral PFJ cartilage damage in limbs with forefoot varus and valgus were determined using logistic regression. The relationship between increasing varus alignment and increasing odds of medial and lateral PFJ cartilage damage was assessed. Of the 51% of limbs with forefoot varus, 91.3% had medial, and 78.3% had lateral PFJ cartilage damage, compared with 54.6% and 68.2% of those with forefoot valgus. The former also had 3.0 times (95% CI 1.2, 7.7) the odds of medial PFJ damage; no association was found with lateral damage (OR 1.4, 95% CI 0.7, 3.0). Feet in the highest tertile of varus alignment had 3.9 times (95% CI 10, 15.3, P = 0.058) the odds of medial PFJ damage as those in the lowest tertile. The results of this study suggest a relationship between forefoot varus and medial PFJ cartilage damage in older adults. As forefoot varus may be modified with foot orthoses, these findings indicate a potential role for orthoses in the treatment of medial PFJ OA. Anat Rec, 300:1032-1038, 2017. © 2016 Wiley Periodicals, Inc.

Robot Manipulator Control Using PLC with Position Based and Image Based Algorithm

Programmable Logic Controller is making big role in automation and robotics. This paper described about the design and implementation of Artificial intelligence algorithms for controlling the robotic arm or manipulator hardware platform using Programmable Logic Controller (PLC). The controlled robot is 5 degrees of freedom (DOF) manipulator with a closed kinematic chain, designed for high-performance pick and place applications. The control software is fully developed on a commercial PLC system, using its standard programming tools and the multi-tasking features of its operating system. In particular, the paper analyse in detail the drawbacks and the advantages related to the choice of standard PLCs in this kind of applications, compared to the much common choice of specialized hardware or industrial personal computers, with particular emphasis on the computational performances obtained with the proposed control architecture.

Passive Rehabilitation Exercises with an Ankle Rehabilitation Prototype Based in a Robot Parallel Structure

In this paper the implementation of PID controllers for the development of passive rehabilitation exercises are presented. For which it is designed and built an ankle rehabilitation prototype based on a structure of parallel robot with a mechanism of the type 2-RRSP (two closed kinematic chains and consisting of joints: revolute-revolute-sphere in slot- fixed post with sphere). Free software is used to develop the computer programs associated with rehabilitation exercises. Regarding the laboratory testing stage, the results of passive exercises are reported, in these exercises path planning is included and PID control is used, for inversion-eversion, dorsal-plantar flexion and combined movements.

Simulation of Constrained Musculoskeletal Systems in Task Space.

This paper proposes an operational task space formalization of constrained musculoskeletal systems, motivated by its promising results in the field of robotics. The change of representation requires different algorithms for solving the inverse and forward dynamics simulation in the task space domain. We propose an extension to the direct marker control and an adaptation of the computed muscle control algorithms for solving the inverse kinematics and muscle redundancy problems, respectively. Experimental evaluation demonstrates that this framework is not only successful in dealing with the inverse dynamics problem, but also provides an intuitive way of studying and designing simulations, facilitating assessment prior to any experimental data collection. The incorporation of constraints in the derivation unveils an important extension of this framework toward addressing systems that use absolute coordinates and topologies that contain closed kinematic chains. Task space projection reveals a more intuitive encoding of the motion planning problem, allows for better correspondence between observed and estimated variables, provides the means to effectively study the role of kinematic redundancy, and most importantly, offers an abstract point of view and control, which can be advantageous toward further integration with high level models of the precommand level. Task-based approaches could be adopted in the design of simulation related to the study of constrained musculoskeletal systems.

Modeling and PDC fuzzy control of planar parallel robot

Many works in the literature have studied the kinematical and dynamical issues of parallel robots. But it is still difficult to extend the vast control strategies to parallel mechanisms due to the complexity of the model-based control. This complexity is mainly caused by the presence of multiple closed kinematic chains, making the system naturally described by a set of differential–algebraic equations. The aim of this work is to control a two-degree-of-freedom parallel manipulator. A mechanical model based on differential–algebraic equations is given. The goal is to use the structural characteristics of the mechanical system to reduce the complexity of the nonlinear model. Therefore, a trajectory tracking control is achieved using the Takagi-Sugeno fuzzy model derived from the differential–algebraic equation forms and its linear matrix inequality constraints formulation. Simulation results show that the proposed approach based on differential–algebraic equations and Takagi-Sugeno fuzzy modeling leads to a better robustness against the structural uncertainties.

Structural synthesis and analysis of multiple-jointed mechanical systems and industrial application for robot manipulator

The paper proposes the structural synthesis method for generation of closed kinematic chains with all the possible kinds of multiple joints according to the given number K- independent loops up to the maximum multiple joint factor Vmax(K). Firstly, the structural synthesis method of non-fractionated and fractionated multiple joint kinematic chains based on the combination of corresponding simple and multiple joints is presented. Secondly, the atlas database with all the possible kinds of multiple joints containing various 3 (case K = 2) and 9 (case K = 3) multiple joint non-fractionated and fractionated structures is established and illustrated. Thirdly, all the possible multiple joint assortments ([M.J.A.]) for non-fractionated as well as fractionated multiple joint kinematic chains up to K = 3 and Vmax = 4 are synthesized and revealed for the first time. Finally, the structural analysis of multiple joint kinematic chains with the maximum total multiple joint factor for industrial applications in robotics is performed.

Effect of Close Kinematic Chain Exercises on Upper Limb Spasticity in Hemiparetic Adult

Effect of Close Kinematic Chain Exercises on Upper Limb Spasticity in Hemiparetic Adult

An automatic method for the connectivity calculation in planar closed kinematic chains

In the initial stage of the creative design of some specific mechanisms such as the parallel manipulator, the connectivity between the base and the end-effector must satisfy the requirement. This paper proposes a new method for the connectivity calculation between two links, based on which an automatic method to acquire the connectivity matrix for planar closed kinematic chains is developed with the aid of C++ programming language. The method has several advantageous features resulting in lower complexity relative to the methods presented in the literature. The whole process to compute connectivity matrix using Floyd-Warshall algorithm, depth-first search (DFS) algorithm and the subchain mobility superposition algorithm is presented and the planar kinematic chains with up to 6 independent loops, together with the ones found in literature, are illustrated to show the validity and efficiency of the method. This method can build a convenient bridge to automatically generate the mechanisms, whose base and end-effector have the required connectivity, from the synthesized kinematic chains.

Relationships between movements of the lower limb joints and the pelvis in open and closed kinematic chains during a gait cycle.

Lots of athletic skills performed during practice or competition are initiated by the legs, where athletes either walk or run prior to executing specific skills. Kinematic chains are used to describe the relationships between body segments and joints during movement. The aim of this study was to determine the relationships between movements of lower limb segments and the pelvis in open and closed kinematic chains while walking. The experimental group consisted of 32 males (age 23.3 ± 2.5 years, body mass 78.1 ± 8.7 kg, body height 182 ± 6 cm). For 3D analysis, an optoelectronic system Vicon MX (7 cameras, frequency 200 Hz) was used. Positioning of the segments was determined by the PlugInGait Model. Each participant executed five trials at speeds ranging from 1.38 to 1.52 m·s-1. The relationships between angle variables of the lower limbs and the pelvis in selected gait cycle phases were evaluated using STATISTICA software (version 10.0) and the Spearman correlation. The highest numbers of moderate and large correlations were found at opposite toe off, heel rise and initial contact for the sagittal and transversal planes in comparison to the frontal plane. The closed kinematic chain had a stronger impact on determining the movement pattern. The instructions or interventions focusing on closed kinematic chain alternation are more effective for changes in a movement pattern. The preferred limb initiates kinematics in the direction of propulsion, while the non-preferred limb in internal and external rotation.

Synthesis of the Four-Bar Double-Constraint Mechanisms by the Application of the Grubler's Method

The paper provides investigations on the structural synthesis of kinematic schemes of a spatial double-constraint mechanisms with one DOF. The investigations have been carried out with the use of the Grubler's method. The Grubler's condition for planar closed kinematic chains was developed for spatial chains including two general imposed constraints with consideration of relative movements and kinematic pairs. By means of introduction of two rotative joints, one screw pair and one cylindrical joint two different variations of spatial four-bar closed kinematic chains have been designed in the current investigation. Six kinematic schemes of non-isomorphic one DOF mechanisms have been designed from these two chains by fixing one link. The approach offered in this paper can be applied for the structural synthesis of spatial mechanisms from other families in accordance with the used kinematic pairs and numbers of imposed constraints.