scholarly journals Kinematics Analysis and Singularity Avoidance of a Parallel Mechanism with kinematic redundancy

2021 ◽  
Author(s):  
chaoyu shen ◽  
Haibo Qu ◽  
Sheng Guo ◽  
Xiao Li
Keyword(s):  
Theoretical Analysis ◽  
Parallel Mechanism ◽  
Jacobian Matrix ◽  
Fault Tolerant ◽  
Degree Of Freedom ◽  
Kinematics Analysis ◽  
Kinematic Redundancy ◽  
Inverse Solutions ◽  
Three Degree Of Freedom ◽  
Actuated Joints

Abstract The kinematic redundancy is considered as a way to improve the performance of parallel mechanism. In this paper, the kinematics performance of a three degree-of-freedom parallel mechanism with kinematic redundancy (3-DOF PM-KR) and the influence of redundant part on the PM-KR are analyzed. Firstly, the kinematics model of the PM-KR is established. The inverse solutions, the Jacobian matrix and the workspace of the PM-KR are solved. Secondly, the influence of the redundant redundancy on the PM-KR has been analyzed. Since there exists kinematic redundancy, the PM-KR possesses the fault-tolerant performance. By locking one actuated joint or two actuated joints simultaneously, the fault-tolerant workspace are obtained. When the position of the redundant part is changed, the workspace and singularity will be changed. The results show that the kinematic redundancy can be used to avoid the singularity. Finally, the simulations are performed to prove the theoretical analysis.

Novel Design and Analysis of a Fully Decoupled 3-DOF Spherical Parallel Robot

2009 ◽  
Author(s):  
Dan Zhang ◽  
Fan Zhang
Keyword(s):  
Physical Meaning ◽  
Parallel Mechanism ◽  
Jacobian Matrix ◽  
Parallel Robot ◽  
Degree Of Freedom ◽  
Redundant Constraints ◽  
Rotational Motions ◽  
Three Degree Of Freedom ◽  
Novel Design

In this paper, we propose a unique, decoupled Three Degree-of-Freedom (DOF) parallel wrist. The condition required for synthesizing a fully isotropic parallel mechanism is obtained based on the physical meaning of the row vector in the Jacobian Matrix. Specifically, an over-constrained spherical 3-DOF parallel mechanism is presented and the modified structure, which avoids the redundant constraints, is also introduced. The proposed manipulator is capable of decoupled rotational motions around the x, y and z axes and contains an output angle that is equal to the input angle. Since this device is analyzed with the Jacobian Matrix, which is constant, the mechanism is free of singularity and maintains homogenous stiffness over the entire workspace.

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.

A novel 4-RRCR parallel mechanism based on screw theory and its kinematics analysis

2012 ◽  
Vol 227 (9) ◽  
pp. 2039-2048 ◽  
Author(s):  
Sheng Guo ◽  
Congzhe Wang ◽  
Haibo Qu ◽  
Yuefa Fang
Keyword(s):  
Parallel Mechanism ◽  
Jacobian Matrix ◽  
Screw Theory ◽  
Degree Of Freedom ◽  
Forward Kinematics ◽  
Kinematics Analysis ◽  
Elimination Method ◽  
Direct Kinematics

In this article, a novel 4-RRCR parallel mechanism is introduced based on screw theory, and its kinematics and singularity are studied systematically. First, the degree of freedom analysis is performed using the screw theory. The formulas for solving the inverse and direct kinematics are derived. Second, a recursive elimination method is proposed to solve the Jacobian matrix based on the algebra operation of reciprocal product. Then, three kinds of singularity, i.e. limb, platform, and actuation singularities are analyzed. Finally, the analysis proves that the proposed mechanism possesses two advantages of simple forward kinematics and no platform singularity.

Design of a Redundantly Actuated Asymmetric Linear DELTA Parallel Mechanism for Singularity-Free Mode Changes

2014 ◽  
Vol 575 ◽  
pp. 711-715 ◽  
Author(s):  
Takashi Harada
Keyword(s):  
Numerical Simulations ◽  
Parallel Mechanism ◽  
Jacobian Matrix ◽  
Degree Of Freedom ◽  
Moving Plate ◽  
Mode Change ◽  
Redundantly Actuated ◽  
Free Mode ◽  
Linear Actuators ◽  
Three Degree Of Freedom

A novel parallel mechanism which enlarges the workspace by singularity-free mode change is proposed. The proposed mechanism is inherited the design of Linear DELTA which has three degree-of-freedom translational moving plate driven by three linear actuators, in addition, extended it by redundantly actuation by four linear actuators and asymmetric design. New criterions about redundancy and singularity of redundantly actuated parallel mechanism using summation and product of determinants of minor matrices of the transposed Jacobian matrix are proposed. Redundantly actuation and asymmetric design enables singularity-free mode changes with loss redundancy but maintain non-singularity, that are evaluated by the proposed criterions. Numerical simulations demonstrate the singularity-free mode changes of the proposed mechanism.

Parametric Design of a Spherical Eight-Bar Linkage Based on a Spherical Parallel Manipulator

2008 ◽  
Vol 1 (1) ◽  
Author(s):  
Gim Song Soh ◽  
J. Michael McCarthy
Keyword(s):  
Inverse Kinematics ◽  
Parallel Manipulator ◽  
Parametric Design ◽  
Degree Of Freedom ◽  
Kinematics Analysis ◽  
End Effector ◽  
Arbitrary Base ◽  
Three Degree Of Freedom ◽  
Spherical Parallel Manipulator

This paper presents a procedure that determines the dimensions of two constraining links to be added to a three degree-of-freedom spherical parallel manipulator so that it becomes a one degree-of-freedom spherical (8, 10) eight-bar linkage that guides its end-effector through five task poses. The dimensions of the spherical parallel manipulator are unconstrained, which provides the freedom to specify arbitrary base attachment points as well as the opportunity to shape the overall movement of the linkage. Inverse kinematics analysis of the spherical parallel manipulator provides a set of relative poses between all of the links, which are used to formulate the synthesis equations for spherical RR chains connecting any two of these links. The analysis of the resulting spherical eight-bar linkage verifies the movement of the system.

Architecture Optmization of a 3-DOF Parallel Mechanism

1998 ◽  
Author(s):  
J. A. Carretero ◽  
R. P. Podhorodeski ◽  
M. Nahon
Keyword(s):  
Parallel Mechanism ◽  
Architectural Design ◽  
Degrees Of Freedom ◽  
Jacobian Matrix ◽  
Design Parameters ◽  
Objective Functions ◽  
Constraint Equations ◽  
Three Degree Of Freedom ◽  
Architecture Optimization ◽  
Three Degrees Of Freedom

Abstract This paper presents a study of the architecture optimization of a three-degree-of-freedom parallel mechanism intended for use as a telescope mirror focussing device. The construction of the mechanism is first described. Since the mechanism has only three degrees of freedom, constraint equations describing the inter-relationship between the six Cartesian coordinates are given. These constraints allow us to define the parasitic motions and, if incorporated into the kinematics model, a constrained Jacobian matrix can be obtained. This Jacobian matrix is then used to define a dexterity measure. The parasitic motions and dexterity are then used as objective functions for the optimizations routines and from which the optimal architectural design parameters are obtained.

Determination of the Singularity Loci of Spherical Three-Degree-of-Freedom Parallel Manipularors

1992 ◽  
Author(s):  
Clément M. Gosselin ◽  
Jaouad Sefrioui
Keyword(s):  
Graphical Representation ◽  
Jacobian Matrix ◽  
Parallel Manipulators ◽  
Degree Of Freedom ◽  
End Effector ◽  
Cartesian Space ◽  
Singularity Locus ◽  
Three Degree Of Freedom ◽  
Analytical Expressions

Abstract In this paper, an algorithm for the determination of the singularity loci of spherical three-degree-of-freedom parallel manipulators with prismatic atuators is presented. These singularity loci, which are obtained as curves or surfaces in the Cartesian space, are of great interest in the context of kinematic design. Indeed, it has been shown elsewhere that parallel manipulators lead to a special type of singularity which is located inside the Cartesian workspace and for which the end-effector becomes uncontrollable. It is therfore important to be able to identify the configurations associated with theses singularities. The algorithm presented is based on analytical expressions of the determinant of a Jacobian matrix, a quantity that is known to vanish in the singular configurations. A general spherical three-degree-of-freedom parallel manipulator with prismatic actuators is first studied. Then, several particular designs are investigated. For each case, an analytical expression of the singularity locus is derived. A graphical representation in the Cartesian space is then obtained.

Design and analysis of a totally decoupled 3-DOF spherical parallel manipulator

Robotica ◽  
2010 ◽  
Vol 29 (7) ◽  
pp. 1093-1100 ◽  
Author(s):  
Dan Zhang ◽  
Fan Zhang
Keyword(s):  
Physical Meaning ◽  
Parallel Mechanism ◽  
Parallel Manipulator ◽  
Jacobian Matrix ◽  
Degree Of Freedom ◽  
Redundant Constraints ◽  
Rotational Motions ◽  
Spherical Parallel Manipulator

SUMMARYIn this paper, we propose a unique, decoupled 3 degree-of-freedom (DOF) parallel wrist. The condition required for synthesizing a fully isotropic parallel mechanism is obtained on the basis of the physical meaning of the row vector in the Jacobian matrix. Specifically, an over-constrained spherical 3-DOF parallel mechanism is presented and the modified structure, which avoids the redundant constraints, is also introduced. The proposed manipulator is capable of decoupled rotational motions around the x, y, and z axes and contains an output angle that is equal to the input angle. As this device is analyzed with the Jacobian matrix, the mechanism is free of singularity within its workspace and maintains homogenous stiffness over the entire workspace.

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.

Synthesis, Design, and Prototyping of a Planar Three Degree-of-Freedom Reactionless Parallel Mechanism

2004 ◽  
Vol 126 (6) ◽  
pp. 992-999 ◽  
Author(s):  
Simon Foucault ◽  
Cle´ment M. Gosselin
Keyword(s):  
Parallel Mechanism ◽  
Degree Of Freedom ◽  
Numerical Verification ◽  
Dynamic Balancing ◽  
Synthesis Design ◽  
Reaction Forces ◽  
Three Degree Of Freedom

This paper addresses the dynamic balancing of a planar three-degree-of-freedom parallel mechanism. A mechanism is said to be dynamically balanced if, for any motion of the mechanism, the reaction forces and torques at the base are identically equal to zero, at all times. The proposed mechanism is based on legs consisting of five-bar parallelogram linkages. The balancing equations are first obtained. Then, optimization is used in order to minimize the mass and inertia of the moving links. Finally, a numerical verification of the dynamic balancing is provided and the prototype is presented.

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