Analysis and Simulation of Velocity and Acceleration Based on Three-Translational Parallel Mechanism

2011 ◽  
Vol 299-300 ◽  
pp. 940-944
Author(s):  
Dong Tao Xu ◽  
Zhi Li Sun ◽  
Yong Ying Du
Keyword(s):  
Theoretical Calculation ◽  
Analytical Method ◽  
Parallel Mechanism ◽  
Jacobian Matrix ◽  
Virtual Prototyping ◽  
Vector Method ◽  
Kinematic Simulation ◽  
Operating Data ◽  
Moving Platform

Aimed at three-translational parallel mechanism, the velocity Jacobian matrix is formulated on the basis of analytical method, so the velocity and acceleration of the moving platform is calculated. Then the velocity and acceleration formulas of all components’ centroids are deduced based on the vector method. The above formulas are very simple and easy to solve. Kinematic simulation is carried out by ADAMS virtual prototyping software. The operating data is obtained, it verifies the correctness of the theoretical calculation.

Kinematic Analysis and Simulation of the Translational Parallel Mechanism

2011 ◽  
Vol 213 ◽  
pp. 43-47 ◽  
Author(s):  
Dong Tao Xu ◽  
Zhi Li Sun ◽  
Jia Lian Shi
Keyword(s):  
Kinematic Analysis ◽  
Parallel Mechanism ◽  
Virtual Prototyping ◽  
Inverse Solution ◽  
Kinematic Modeling ◽  
Forward Solution ◽  
Vector Method ◽  
End Effector ◽  
Kinematic Simulation ◽  
Revolute Joints

This paper presents a novel, precision, maneuverable, 3-DOF translational parallel mechanism. The mechanism’s important feature is that all of the kinematic joints are the revolute joints. The paper derives the mechanism’s kinematic forward solution and inverse solution by using of coordinate transformation elimination method and vector method, and establishes proper kinematic modeling. Kinematic simulation is carried out by ADAMS virtual prototyping software. The operating data is obtained, it verifies the correctness of solving the forward and inverse solution, and solve the question of choices for many results during the theoretical solution. This technique can provide a useful tool in the design of kinematic trajectory of the parallel mechanism’s end-effector and the kinematic analysis of other parallel mechanism.

KINEMATICS AND WORKSPACE ANALYSIS OF A 3 DEGREE OF FREEDOM PARALLEL MECHANISM WITH PARALLELOGRAM LINKAGE

2017 ◽  
Vol 41 (5) ◽  
pp. 922-935
Author(s):  
HongJun San ◽  
JunSong Lei ◽  
JiuPeng Chen ◽  
ZhengMing Xiao ◽  
JunJie Zhao
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Analytical Method ◽  
Theoretical Basis ◽  
Parallel Mechanism ◽  
Graphical Method ◽  
Degree Of Freedom ◽  
Workspace Analysis ◽  
Fixed Base ◽  
Moving Platform

In this paper, a 3-DOF translational parallel mechanism with parallelogram linkage was studied. According to the space vector relation between the moving platform and the fixed base, the direct and inverse position solutions of this mechanism was deduced through analytical method. In addition, the error of the algorithm was analyzed, and the algorithm had turned out to be effective and to have the satisfactory computational precision. On the above basis, the workspace of this mechanism was found through graphical method, which was compared with that of finding through Monte Carlo method, and there was the feasibility for analyzing the workspace of the mechanism by graphical method. The characteristic of the mechanism was analyzed by comparing the results of two analysis methods, which provided a theoretical basis for the application of the mechanism.

Geometry and Kinematic Analysis of a Redundantly Actuated Parallel Mechanism for Rehabilitation

2007 ◽  
Author(s):  
Jody A. Saglia ◽  
Jian S. Dai
Keyword(s):  
Control System ◽  
Kinematic Analysis ◽  
Parallel Mechanism ◽  
Parallel Manipulator ◽  
Jacobian Matrix ◽  
Forward Kinematics ◽  
Control System Design ◽  
Ankle Rehabilitation ◽  
Redundantly Actuated ◽  
Moving Platform

This paper presents the geometry and the kinematic analysis of a parallel manipulator developed for ankle rehabilitation, as the beginning of a control system design process. First the geometry of the parallel mechanism is described, secondly the equations for the inverse and the forward kinematics are obtained, then the forward kinematics is analyzed in order to define all the possible configurations of the moving platform. Finally the Jacobian matrix of the rig is obtained by differentiating the position equations and the singularities are investigated, comparing the non-redundant and redundant type of mechanism.

Design and Kinematics Analysis of a Novel Planar Parallel Mechanism

2014 ◽  
Vol 568-570 ◽  
pp. 904-910
Author(s):  
Yan Bin Zhang ◽  
Hui Ping Wang
Keyword(s):  
Condition Number ◽  
Parallel Mechanism ◽  
Jacobian Matrix ◽  
Screw Theory ◽  
Kinematics Analysis ◽  
Moving Platform ◽  
One To One ◽  
Actuated Joints

A novel 3-dof planar parallel mechanism, which is composed by three different limbs, is designed. The moving platform can translate along two directions and rotate around one axis with respect to the base. Mobility of the mechanism is discussed and calculated based on the screw theory. The forward and the inverse analytical position equations are derived and the veloctiy analysis is addressed too. The Jacobian matrix is an identical one, so there exists one-to-one corresponding linear controlling relationship between one of the actuated joints and one of the outputs of the platform. Moreover, the condition number of the Jacobian matrix is constantly equal to one and the mechanism shows fully-isotropic throughout entire workspace.

Error Analysis of a 2-PRS/2-UPS 4-DOF Parallel Platform

2012 ◽  
Vol 605-607 ◽  
pp. 1511-1514
Author(s):  
Shan Le Cai ◽  
Li Bing Peng ◽  
Wen Tao Huang
Keyword(s):  
Error Compensation ◽  
Parallel Mechanism ◽  
Theoretical Foundation ◽  
Error Modeling ◽  
Vector Method ◽  
Joint Point ◽  
Structural Error ◽  
New Type ◽  
Parallel Platform ◽  
Moving Platform

A new type of a 2-PRS/2-UPS 4-DOF parallel platform was introduced. The error model of the parallel worktable was established through the vector method. The effect of structural error, driving error, position error and clearance error of the joint point to the pose error of the moving platform can be analyzed. Error modeling provides theoretical foundation for design and error compensation of the parallel mechanism.

scholarly journals Kinematic analysis of a novel 3-CRU translational parallel mechanism

2015 ◽  
Vol 6 (1) ◽  
pp. 57-64 ◽  
Author(s):  
B. Li ◽  
Y. M. Li ◽  
X. H. Zhao ◽  
W. M. Ge
Keyword(s):  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Jacobian Matrix ◽  
Screw Theory ◽  
Structural Characteristics ◽  
Parallel Mechanisms ◽  
Reachable Workspace ◽  
Potential Applications ◽  
Moving Platform ◽  
And Performance

Abstract. In this paper, a modified 3-DOF (degrees of freedom) translational parallel mechanism (TPM) three-CRU (C, R, and U represent the cylindrical, revolute, and universal joints, respectively) structure is proposed. The architecture of the TPM is comprised of a moving platform attached to a base through three CRU jointed serial linkages. The prismatic motions of the cylindrical joints are considered to be actively actuated. Kinematics and performance of the TPM are studied systematically. Firstly, the structural characteristics of the mechanism are described, and then some comparisons are made with the existing 3-CRU parallel mechanisms. Although these two 3-CRU parallel mechanisms are both composed of the same CRU limbs, the types of freedoms are completely different due to the different arrangements of limbs. The DOFs of this TPM are analyzed by means of screw theory. Secondly, both the inverse and forward displacements are derived in closed form, and then these two problems are calculated directly in explicit form. Thereafter, the Jacobian matrix of the mechanism is derived, the performances of the mechanism are evaluated based on the conditioning index, and the performance of a 3-CRU TPM changing with the actuator layout angle is investigated. Thirdly, the workspace of the mechanism is obtained based on the forward position analysis, and the reachable workspace volume is derived when the actuator layout angle is changed. Finally, some conclusions are given and the potential applications of the mechanism are pointed out.

The Statics Analysis and Verification of 3-DOF Parallel Mechanism Based on Two Methods

2013 ◽  
Vol 7 (2) ◽  
pp. 237-244 ◽  
Author(s):  
Guangda Lu ◽  
◽  
Aimei Zhang ◽  
Jing Zhou ◽  
Shigang Cui ◽  
...  
Keyword(s):  
Force Feedback ◽  
Jacobian Matrix ◽  
Virtual Work ◽  
Rehabilitation Robot ◽  
Principle Of Virtual Work ◽  
Equilibrium Equations ◽  
Vector Method ◽  
Ankle Rehabilitation ◽  
Moving Platform ◽  
Mathematical Relationships

Statics of the 3-RSS/S parallel ankle-rehabilitation robot is analyzed in this paper using two methods, i.e. the component vector method and the principle of virtual work. Static equilibrium equations based on component vector theory were established on a moving platform, and cranks of 3-RSS/S parallel Ankle-rehabilitation Robot, using this method, to obtain mathematical relationships between the external torque of moving platform and the output torque of three cranks. The velocity Jacobian matrix of the robot is calculated firstly using the principle of virtual work method, then the force Jacobian matrix is obtained based on the relationship between velocity Jacobian matrix and force Jacobian matrix. The results of the two methods are verified and found to be consistent by calculation, and the force Jacobian matrix of the robot is the basis of the force feedback control for the Ankle-rehabilitation Robot.

Continuous motion of a novel 3-CRC symmetrical parallel mechanism

2015 ◽  
Vol 230 (3) ◽  
pp. 392-405 ◽  
Author(s):  
Ziming Chen ◽  
Wen-ao Cao ◽  
Huafeng Ding ◽  
Zhen Huang
Keyword(s):  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Jacobian Matrix ◽  
Parallel Mechanisms ◽  
Numerical Examples ◽  
Parasitic Motion ◽  
Continuous Rotation ◽  
Moving Platform ◽  
Motion Characteristics ◽  
Three Degrees Of Freedom

Parallel mechanisms (PMs) with three degrees of freedom (DOFs) have been studied extensively, especially the PMs with two rotational and one translational DOFs (2R1T PMs). One major problem of the 2R1T PMs is the inherent parasitic motion. In this paper, a novel 2R1T symmetrical parallel mechanism with no parasitic motion is proposed and studied. The moving platform and the base of this mechanism are mirror symmetric with respect to a mid-plane. This moving platform can realize continuous rotation about any axis or any point on the mid-plane and can have continuous translation along the normal line of the mid-plane. The constraint and motion characteristics of this mechanism are analyzed. The kinematics solutions and the Jacobian matrix are derived. The singularities of this PM are discussed. In the end, several numerical examples are given to show the continuous rotations and continuous translations of this PM. This kind of PMs has outstanding advantages of easy path planning and controlling.

Accuracy analysis and synthesis of asymmetric parallel mechanism based on Sobol-QMC

2020 ◽  
Vol 234 (21) ◽  
pp. 4200-4214
Author(s):  
Mengli Wu ◽  
Xianqu Yue ◽  
Weibin Chen ◽  
Qi Nie ◽  
Yue Zhang
Keyword(s):  
Parallel Mechanism ◽  
Closed Loop ◽  
Jacobian Matrix ◽  
Mapping Function ◽  
Error Modeling ◽  
Accuracy Analysis ◽  
Vector Method ◽  
Evaluation Indexes ◽  
Quasi Monte Carlo ◽  
Analysis And Synthesis

Aiming at the aircraft composite skin grinding, a new three degree-of-freedom (DOF) parallel mechanism with asymmetrical structure (TAM) is proposed to replace manual grinding. The TAM is achieved by integrating one of active limbs into the passive limb while keeping the required DOF unchanged, which is divided into two closed-loop chains: telescopic rod and parallelogram. The inverse kinematics models of the two chains are established according to closed-loop vector method. Thus, the actuation and the constraint Jacobian matrix are obtained. Based on the perturbation principle, the error modeling of the TAM is built. Adopting the constraint Jacobian matrix, 15 uncompensated errors are distinguished from the error model. In order to improve the working accuracy of the TAM, accuracy analysis and synthesis are necessary for all the uncompensated errors. The mapping function reflects the influence of uncompensated errors on the pose accuracy. The global sensitivity evaluation indexes are established by mapping function. Since Sobol sequences are superior in uniformity and convergence, the Quasi-Monte Carlo method based on Sobol sequences (Sobol-QMC) is introduced for sensitivity analysis. Taking the minimum manufacturing and installation costs as the optimization target, the objective function of accuracy synthesis is constructed. Ultimately, the reasonable tolerance zone of each uncompensated error is calculated by genetic algorithm. Simulation is performed by Sobol-QMC to verify the rationality of the optimization. The results show the probability is above 97% where most pose errors are in [[Formula: see text], [Formula: see text]] within the workspace. Therefore, accuracy synthesis is correct and practical.

Forward and Inverse Position Solution Analysis of 2UPR/1SPR 3-DOF Parallel Mechanism

2012 ◽  
Vol 605-607 ◽  
pp. 1573-1576
Author(s):  
Hong Jun San ◽  
Yuan Ming Wang ◽  
Jian Xiong Liu
Keyword(s):  
Numerical Method ◽  
Analytical Method ◽  
Parallel Mechanism ◽  
Structural Constraint ◽  
Moving Platform ◽  
Position Solution

In this paper, forward and inverse position solution are analyzed for a novel 2UPR/1SPR special 3-DOF parallel mechanism. The moving platform of this mechanism have 1 translational DOF and 2 rotational DOFs. The inverse position solution of this mechanism was deduced by analytical method. The decoupling equation of position and posture parameters are formulated on the basis of structural constraint of the concerned mechanism. The forward position solution of this mechanism is achieved by numerical method.

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