Examination and comparison of different methods to model closed loop kinematic chains using Lagrangian formulation with cut joint, clearance joint constraint and elastic joint approaches

2021 ◽  
Vol 160 ◽  
pp. 104294 ◽  
Author(s):  
Filipe Marques ◽  
Ivo Roupa ◽  
Miguel T. Silva ◽  
Paulo Flores ◽  
Hamid M. Lankarani
Keyword(s):  
Closed Loop ◽  
Lagrangian Formulation ◽  
Joint Clearance ◽  
Kinematic Chains ◽  
Elastic Joint ◽  
Clearance Joint

Efficient Human Motion Planning Using Recursive Dynamics and Optimal Control Techniques

1999 ◽  
Author(s):  
Janzen Lo ◽  
Dimitris Metaxas
Keyword(s):  
Optimal Control ◽  
Motion Planning ◽  
Closed Loop ◽  
High Efficiency ◽  
Human Motion ◽  
Lagrangian Formulation ◽  
Planning Problem ◽  
Tree Structures ◽  
Recursive Dynamics ◽  
Minimum Torque

Abstract We present an efficient optimal control based approach to simulate dynamically correct human movements. We model virtual humans as a kinematic chain consisting of serial, closed-loop, and tree-structures. To overcome the complexity limitations of the classical Lagrangian formulation and to include knowledge from biomechanical studies, we have developed a minimum-torque motion planning method. This new method is based on the use of optimal control theory within a recursive dynamics framework. Our dynamic motion planning methodology achieves high efficiency regardless of the figure topology. As opposed to a Lagrangian formulation, it obviates the need for the reformulation of the dynamic equations for different structured articulated figures. We use a quasi-Newton method based nonlinear programming technique to solve our minimum torque-based human motion planning problem. This method achieves superlinear convergence. We use the screw theoretical method to compute analytically the necessary gradient of the motion and force. This provides a better conditioned optimization computation and allows the robust and efficient implementation of our method. Cubic spline functions have been used to make the search space for an optimal solution finite. We demonstrate the efficacy of our proposed method based on a variety of human motion tasks involving open and closed loop kinematic chains. Our models are built using parameters chosen from an anthropomorphic database. The results demonstrate that our approach generates natural looking and physically correct human motions.

Dynamic Response and Nonlinear Characteristics of Spatial Parallel Mechanism With Spherical Clearance Joint

2019 ◽  
Vol 14 (4) ◽  
Author(s):  
Chen Xiulong ◽  
Li Yuewen ◽  
Jia Yonghao
Keyword(s):  
Dynamic Response ◽  
Contact Force ◽  
Dynamic Equation ◽  
Parallel Mechanism ◽  
Joint Clearance ◽  
Spherical Joint ◽  
Nonlinear Characteristics ◽  
Clearance Joint ◽  
Spatial Parallel Mechanism ◽  
Moving Platform

Spherical joint is a type of common kinematic pair in spatial parallel mechanism. The existence of spherical joint clearance has many adverse effects on the mechanism. A method of forecasting the dynamic behaviors of spatial parallel mechanism with spherical clearance joint is proposed. The 4-UPS-UPU spatial parallel mechanism with spherical clearance is taken as the research object, the dynamic response, and nonlinear characteristics of the mechanism are studied. The kinematic model and the contact force model of the spherical clearance are established. The dynamic equation of the spatial parallel mechanism with spherical joint clearance is derived by Newton–Euler method. The above-mentioned dynamic equation is solved by using the ODE113 function that is based on a variable order numerical differential algorithm in matlab. The dynamic responses of moving platform with different clearance values are analyzed. The contact force and the center trajectory of the sphere at the spherical joint are obtained. In addition, the phase trajectory, Poincare map, and bifurcation diagram are analyzed, and the nonlinear characteristics of the spherical clearance joint and the moving platform are obtained. By comparing the results, such as the acceleration of moving platform and the contact force, with virtual prototype simulation, the correctness of the dynamic equation of the spatial parallel mechanism with spherical clearance joint and the analysis results are verified. The researches show that the change of clearance value has a great influence on the motion state of spherical clearance joint, and chaos phenomena appears in the clearance joint with the increase in the clearance value. And the impact phenomenon appears between the spherical joint elements, which makes the mechanism generated vibration.

A DOE- and Kriging-Based Model for Studying on the Dynamics of Multibody Mechanical Systems With Revolute Joint Clearance

2013 ◽  
Author(s):  
Zhenhua Zhang ◽  
Liang Xu ◽  
Paulo Flores ◽  
Hamid M. Lankarani
Keyword(s):  
Simulation Model ◽  
Mechanical System ◽  
Contact Force ◽  
Design Parameter ◽  
Joint Clearance ◽  
Design Parameters ◽  
Force Model ◽  
Revolute Joint ◽  
Clearance Joint ◽  
Contact Force Model

Over the last two decades, extensive work has been conducted on dynamic effect of joint clearances in multibody mechanical systems. In contrast, little work has been devoted to optimizing the performance of these systems. In this study, analysis of revolute joint clearance is formulated in term of a Hertzian-based contact force model. For illustration, the classical slider-crank mechanism with a revolute clearance joint at the piston pin is presented, and a simulation model is developed using the analysis/design code MSC.ADAMS. The clearance is modeled as a pin-in-a-hole surface-to-surface dry contact, with appropriate contact force model between the joint and bearing surfaces. Different simulations are performed to demonstrate the influence of the joint clearance size and the input crank speed on the dynamic behavior of the system with the clearance joint. An innovative design-of-experiment (DOE)-based method for optimizing the performance of a mechanical system with the revolute joint clearance for different ranges of design parameters is then proposed. Based on the simulation model results from sample points, which are selected by a Latin hypercube sampling (LHS) method, a polynomial function Kriging meta-model is established instead of the actual simulation model. The reason for development and use of the meta-model is to bypass computationally intensive simulations of a computer model for different design parameter values in place of a more efficient and cost-effective mathematical model. Finally, numerical results obtained from two application examples, considering the different design parameters, including the joint clearance size, crank speed, and contact stiffness, are presented for further analyzing the dynamics of the revolute clearance joint in a mechanical system. This allows for predicting the influence of design parameter changes, in order to minimize contact forces, accelerations, and power requirements due to the existence of joint clearance.

A Novel Method on Singularity Analysis in Parallel Manipulators

2006 ◽  
Author(s):  
Hodjat Pendar ◽  
Maryam Mahnama ◽  
Hassan Zohoor
Keyword(s):  
Closed Loop ◽  
Parallel Manipulators ◽  
Singularity Analysis ◽  
Parallel Mechanisms ◽  
Kinematic Chains ◽  
Working Space ◽  
Novel Approach ◽  
Main Technique ◽  
Novel Method ◽  
Constraint Plane

A parallel manipulator is a closed loop mechanism in which a moving platform is connected to the base by at least two serial kinematic chains. The main problem engaged in these mechanisms, is their restricted working space as a result of singularities. In order to tackle these problems, many methods have been introduced by scholars. However, most of the mentioned methods are too much time consuming and need a great amount of computations. They also in most cases do not provide a good insight to the existence of singularity for the designer. In this paper a novel approach is introduced and utilized to identify singularities in parallel manipulators. By applying the new method, one could get a better understanding of geometrical interpretation of singularities in parallel mechanisms. Here we have introduced the Constraint Plane Method (CPM) and some of its applications in parallel mechanisms. The main technique used here, is based on Ceva Theorem.

Equivalent Kinematic Chains of Three Degree-of-Freedom Tripod Mechanisms With Planar-Spherical Bonds

2005 ◽  
Vol 127 (1) ◽  
pp. 95-102 ◽  
Author(s):  
Patrick Huynh ◽  
Jacques M. Herve´
Keyword(s):  
Closed Loop ◽  
Degree Of Freedom ◽  
Robotic Device ◽  
Kinematics Analysis ◽  
Closed Loop System ◽  
Short Introduction ◽  
Kinematic Chains ◽  
Displacement Group ◽  
Three Degree Of Freedom ◽  
Moving Spheres

The paper aims to analyze the equivalent kinematic chains of a family of three-degree-of-freedom (3-DOF) tripod mechanisms with planar-spherical bonds in order to determine the platform motions generated by the mechanisms, and then to develop a prototype of a 3-DOF 3-RPS type parallel mechanism, which can be used as a wrist robotic device. After a short introduction to mechanical generators of Lie subgroups of displacement, the mobility formula of a general 3-DOF tripod mechanism based on the modified Gru¨ebler’s criterion is given. Using displacement group theory theorems, the analyzed closed-loop system becomes finally equivalent to three contacts between a rigid assembly of three moving spheres onto three fixed planes. As an application of the above method, a prototype mechanism is designed and fabricated based on the kinematics analysis, the force capability and the simplicity.

scholarly journals A Kriging Model for Dynamics of Mechanical Systems With Revolute Joint Clearances

2014 ◽  
Vol 9 (3) ◽  
Author(s):  
Zhenhua Zhang ◽  
Liang Xu ◽  
Paulo Flores ◽  
Hamid M. Lankarani
Keyword(s):  
Simulation Model ◽  
Contact Force ◽  
Design Parameter ◽  
Joint Clearance ◽  
Design Parameters ◽  
Force Model ◽  
Revolute Joint ◽  
Clearance Joint ◽  
Contact Force Model ◽  
Joint Clearances

Over the past two decades, extensive work has been conducted on the dynamic effect of joint clearances in multibody mechanical systems. In contrast, little work has been devoted to optimizing the performance of these systems. In this study, the analysis of revolute joint clearance is formulated in terms of a Hertzian-based contact force model. For illustration, the classical slider-crank mechanism with a revolute clearance joint at the piston pin is presented and a simulation model is developed using the analysis/design software MSC.ADAMS. The clearance is modeled as a pin-in-a-hole surface-to-surface dry contact, with an appropriate contact force model between the joint and bearing surfaces. Different simulations are performed to demonstrate the influence of the joint clearance size and the input crank speed on the dynamic behavior of the system with the joint clearance. In the modeling and simulation of the experimental setup and in the followed parametric study with a slightly revised system, both the Hertzian normal contact force model and a Coulomb-type friction force model were utilized. The kinetic coefficient of friction was chosen as constant throughout the study. An innovative design-of-experiment (DOE)-based method for optimizing the performance of a mechanical system with the revolute joint clearance for different ranges of design parameters is then proposed. Based on the simulation model results from sample points, which are selected by a Latin hypercube sampling (LHS) method, a polynomial function Kriging meta-model is established instead of the actual simulation model. The reason for the development and use of the meta-model is to bypass computationally intensive simulations of a computer model for different design parameter values in place of a more efficient and cost-effective mathematical model. Finally, numerical results obtained from two application examples with different design parameters, including the joint clearance size, crank speed, and contact stiffness, are presented for the further analysis of the dynamics of the revolute clearance joint in a mechanical system. This allows for predicting the influence of design parameter changes, in order to minimize contact forces, accelerations, and power requirements due to the existence of joint clearance.

The Influence of Special Positions on the Rigidity of Parallel Structure Mechanisms

2020 ◽  
pp. 21-28
Author(s):  
K.G. Erastova
Keyword(s):  
Closed Loop ◽  
Jacobian Matrix ◽  
Parallel Structure ◽  
Geometrical Parameters ◽  
Chain Mechanism ◽  
Special Position ◽  
Working Zone ◽  
Kinematic Chains ◽  
New Methods ◽  
Promising Area

Due to a sharp increase in the accuracy of manufacturing and quality control of mechanical engineering products, robots based on mechanisms with closed-loop kinematic chains have become a promising area of engineering. One of the advantages of parallel structure mechanisms over serial mechanisms is their increased rigidity. The absence of patterns in the change of rigidity in the working zone and the influence of the so-called special positions necessitate the development of new methods of optimization synthesis of the mechanism. This paper presents an approach based on the Jacobian matrix using which it is possible to determine rigidity in the worst direction of the external force application in each point of the working zone. The same approach can also be used for determining the shape and size of the effective working zone. An example of a flat five-chain mechanism is used to demonstrate the application of the method and obtain a matrix of chain rigidity, construct the parallelogram of forces and determine rigidity distribution in the working zone. It is shown that when approaching a special position, the rigidity of the mechanism decreases ten-fold, and in the special position it equals a zero. The proposed method can be used for optimizing the geometrical parameters of the mechanism on the conditions of maximising the effective working zone.

Approximate Stiffness Modelling and Stiffness Defect Identification for a Heavy-load Parallel Manipulator

Robotica ◽  
2019 ◽  
Vol 37 (6) ◽  
pp. 1120-1142 ◽  
Author(s):  
Shuai Fan ◽  
Shouwen Fan
Keyword(s):  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Joint Clearance ◽  
Contact Deformation ◽  
Heavy Load ◽  
Compliance Matrix ◽  
Defect Identification ◽  
Clearance Joint ◽  
Stiffness Model ◽  
Joint Contact

SummaryWhen using parallel manipulators as machine tools, their stiffness is an important factor in the quality of the produced products. This paper presents an overall approximate stiffness model for a heavy-load parallel manipulator, which considers the effects of actuator stiffness, joint clearance, joint contact deformation, and limb deformation. Based on the principle of virtual work and the introduced modified parameters, the proposed overall compliance matrix successfully takes four factors into a unified expression. To obtain the overall compliance matrix, the approximate stiffness models of the joint clearance, joint contact deformation, and limb deformation are given. In addition, by combining the statistical simulation including the random uncertainties and the proposed approximate stiffness models as the basis of the magnitudes for each random variable, an approach based on the expected trajectory and external load is also proposed for stiffness defect identification such that the estimation is more accurate and reliable. Finally, a numerical example of the 1PU+3UPS parallel manipulator and a discussion are presented to demonstrate the practicability of the proposed stiffness model and defect identification approach. After modifying the structure parameters of the defective components, the prototype experiences a significant stiffness improvement.

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