An Approach to Determining the Unknown Twist/Wrench Subspaces of Lower Mobility Serial Kinematic Chains

2015 ◽  
Vol 7 (3) ◽  
Author(s):  
Tian Huang ◽  
Shuofei Yang ◽  
Manxin Wang ◽  
Tao Sun ◽  
Derek G. Chetwynd
Keyword(s):  
Linear Functional ◽  
Dual Space ◽  
Screw Theory ◽  
Parallel Manipulators ◽  
Dual Basis ◽  
Generalized Jacobian ◽  
Kinematic Chains ◽  
Essential Step ◽  
Effective Manner ◽  
Lower Mobility

Mainly drawing on screw theory and linear algebra, this paper presents an approach to determining the bases of three unknown twist and wrench subspaces of lower mobility serial kinematic chains, an essential step for kinematic and dynamic modeling of both serial and parallel manipulators. By taking the reciprocal product of a wrench on a twist as a linear functional, the underlying relationships among their subspaces are reviewed by means of the dual space and dual basis. Given the basis of a twist subspace of permissions, the causes of nonuniqueness in the bases of the other three subspaces are discussed in some depth. Driven by needs from engineering design, criteria, and a procedure are proposed that enable pragmatic, consistent bases of these subspaces to be determined in a meaningful, visualizable, and effective manner. Three typical examples are given to illustrate the entire process. Then, formulas are presented for the bases of the twist/wrench subspaces of a number of commonly used serial kinematic chains, which can readily be employed for the formulation of the generalized Jacobian of a variety of lower mobility parallel manipulators.

An Approach for Acceleration Analysis of Lower Mobility Parallel Manipulators

2011 ◽  
Vol 3 (1) ◽  
Author(s):  
Haitao Liu ◽  
Tian Huang ◽  
Derek G. Chetwynd
Keyword(s):  
Hessian Matrix ◽  
Parallel Manipulators ◽  
Unified Framework ◽  
Generalized Jacobian ◽  
New Approach ◽  
Kinematic Chains ◽  
Lower Mobility ◽  
Acceleration Analysis ◽  
Definition Of ◽  
Closure Constraints

This paper presents a new approach to the velocity and acceleration analyses of lower mobility parallel manipulators. Building on the definition of the “acceleration motor,” the forward and inverse velocity and acceleration equations are formulated such that the relevant analyses can be integrated under a unified framework that is based on the generalized Jacobian. A new Hessian matrix of serial kinematic chains (or limbs) is developed in an explicit and compact form using Lie brackets. This idea is then extended to cover parallel manipulators by considering the loop closure constraints. A 3-PRS parallel manipulator with coupled translational and rotational motion capabilities is analyzed to illustrate the generality and effectiveness of this approach.

An Approach for Acceleration Analysis of Lower Mobility Parallel Manipulator

2010 ◽  
Author(s):  
Haitao Liu ◽  
Tian Huang ◽  
Derek G. Chetwynd
Keyword(s):  
Parallel Manipulator ◽  
Hessian Matrix ◽  
Parallel Manipulators ◽  
Unified Framework ◽  
Generalized Jacobian ◽  
Kinematic Chains ◽  
Lie Bracket ◽  
Lower Mobility ◽  
Acceleration Analysis ◽  
Definition Of

This paper presents an approach for velocity and acceleration analyses of lower mobility parallel manipulators. Based on the definition of the acceleration motor, the forward/inverse velocity and acceleration equations are formulated with the goal to integrate the relevant analyses under a unified framework based on the generalized Jacobian. A new Hessian matrix of serial kinematic chains (or limb) is developed in an explicit and compact form using Lie bracket. This idea is then extended to cover parallel manipulators by considering the loop closure constraints. A 3-PRS parallel manipulator with coupled translational and rotational moving capabilities is taken as example to illustrate the generality and effectiveness of this approach.

Synthesis of 2T1R Decoupled Parallel Manipulators

2011 ◽  
Vol 308-310 ◽  
pp. 2025-2030 ◽  
Author(s):  
Wen Juan Lu ◽  
Li Jie Zhang ◽  
Da Xing Zeng ◽  
Ruo Song Wang
Keyword(s):  
Screw Theory ◽  
Control Design ◽  
Parallel Manipulators ◽  
Parallel Mechanisms ◽  
Type Synthesis ◽  
Precision Control ◽  
Kinematic Chains ◽  
Step Procedure ◽  
Nonlinear Relation ◽  
Three Degree Of Freedom

For the general parallel mechanisms(PMS), since the coupling between kinematic chains, the nonlinear relation between the input and output is presented, which have led to difficulty in the trajectory planning and precision control. Design of motion decoupled parallel mechanisms(DPMS) has become a good new topic in this area and has captured researcher's attention. In this work, the approach to a synthesis of three degree-of-freedom(3-DOF) DPMS is considered based on screw theory and motion synthesis ideas. Criterions for type synthesis of the branches for DPMS is established according to the twist screw system of the limbs, which assures the decoupling in each limb. Then a six-step procedure is presented for the type synthesis of 2T1R decoupled mechanisms.

scholarly journals Singularity analysis of the H4 robot using Grassmann–Cayley algebra

Robotica ◽  
2012 ◽  
Vol 30 (7) ◽  
pp. 1109-1118 ◽  
Author(s):  
Semaan Amine ◽  
Stéphane Caro ◽  
Philippe Wenger ◽  
Daniel Kanaan
Keyword(s):  
Jacobian Matrix ◽  
Screw Theory ◽  
Parallel Manipulators ◽  
Singularity Analysis ◽  
Analysis Method ◽  
Rank Deficiency ◽  
Constraint Analysis ◽  
Cayley Algebra ◽  
Lower Mobility ◽  
Grassmann Cayley Algebra

SUMMARYThis paper extends a recently proposed singularity analysis method to lower-mobility parallel manipulators having an articulated nacelle. Using screw theory, a twist graph is introduced in order to simplify the constraint analysis of such manipulators. Then, a wrench graph is obtained in order to represent some points at infinity on the Plücker lines of the Jacobian matrix. Using Grassmann–Cayley algebra, the rank deficiency of the Jacobian matrix amounts to the vanishing condition of the superbracket. Accordingly, the parallel singularities are expressed in three different forms involving superbrackets, meet and join operators, and vector cross and dot products, respectively. The approach is explained through the singularity analysis of the H4 robot. All the parallel singularity conditions of this robot are enumerated and the motions associated with these singularities are characterized.

Jacobian-based stiffness analysis method for parallel manipulators with non-redundant legs

2015 ◽  
Vol 230 (3) ◽  
pp. 341-352 ◽  
Author(s):  
Antonius GL Hoevenaars ◽  
Patrice Lambert ◽  
Just L Herder
Keyword(s):  
Parallel Manipulator ◽  
Screw Theory ◽  
Parallel Manipulators ◽  
Structural Elements ◽  
Analysis Method ◽  
End Effector ◽  
Stiffness Analysis ◽  
Compliant Joints ◽  
Lower Mobility ◽  
Actuated Joints

Stiffness is an important element in the model of a parallel manipulator. A complete stiffness analysis includes the contributions of joints as well as structural elements. Parallel manipulators potentially include both actuated joints, passive compliant joints, and zero stiffness joints, while a leg may impose constraints on the end-effector in the case of lower mobility parallel manipulators. Additionally, parallel manipulators are often designed to interact with an environment, which means that an external wrench may be applied to the end-effector. This paper presents a Jacobian-based stiffness analysis method, based on screw theory, that effectively considers all above aspects and which also applies to parallel manipulators with non-redundant legs.

Force/Motion Transmissibility Analysis of Six Degree of Freedom Parallel Mechanisms

2014 ◽  
Vol 6 (3) ◽  
Author(s):  
Tian Huang ◽  
Manxin Wang ◽  
Shuofei Yang ◽  
Tao Sun ◽  
Derek G. Chetwynd ◽  
...  
Keyword(s):  
Linear Functional ◽  
Systematic Approach ◽  
Screw Theory ◽  
Joint Space ◽  
Singular Value ◽  
Parallel Mechanisms ◽  
Dual Basis ◽  
Singular Configurations ◽  
Kinematic Performance ◽  
Six Degree Of Freedom

Drawing mainly on the concepts of dual space and dual basis in linear algebra and on existing screw theory, this paper presents a novel and systematic approach for the force/motion transmissibility analysis of 6DOF parallel mechanisms. By taking the reciprocal product of a wrench on a twist as a linear functional, the property exhibited by the dual basis allows the formulation of the force/motion transmissibility between the joint space and operation space in an accurate and concise manner. The consistency between the force/motion transmissibility and the minimum singular value of the Jacobian for singularity identification is rigorously proved. This leads to the development of a set of homogeneously dimensionless local and global transmission indices for measuring the closeness to singular configurations as well as for kinematic performance evaluation over a given workspace. A Stewart platform is employed an exemplar to illustrate the effectiveness of the approach.

Constraint and Singularity Analysis of Lower-Mobility Parallel Manipulators With Parallelogram Joints

2010 ◽  
Author(s):  
Semaan Amine ◽  
Daniel Kanaan ◽  
Ste´phane Caro ◽  
Philippe Wenger
Keyword(s):  
Projective Space ◽  
Screw Theory ◽  
Parallel Manipulators ◽  
Singularity Analysis ◽  
3 Dimensional ◽  
Geometric Conditions ◽  
Constraint Analysis ◽  
Lower Mobility ◽  
Dimensional Projective Space ◽  
Grassmann Cayley Algebra

This paper presents a general approach to analyze the singularities of lower-mobility parallel manipulators with parallelogram joints. Using screw theory, the concept of twist graph is introduced and the twist graphs of two types of parallelogram joints are established in order to simplify the constraint analysis of the manipulators under study. Using Grassmann-Cayley Algebra, the geometric conditions associated with the dependency of six Plu¨cker vectors of finite and infinite lines in the 3-dimensional projective space are reformulated in the superbracket in order to derive the geometric conditions for parallel singularities. The methodology is applied to three lower-mobility parallel manipulators with parallelogram joints: the Delta-linear robot, the Orthoglide robot and the H4 robot. The geometric interpretations of the singularities of these robots are given.

Type Synthesis of 3-DOF Translational Parallel Manipulators Based on Screw Theory

2004 ◽  
Vol 126 (1) ◽  
pp. 83-92 ◽  
Author(s):  
Xianwen Kong ◽  
Cle´ment M. Gosselin
Keyword(s):  
Screw Theory ◽  
General Procedure ◽  
Linear Equations ◽  
Kinematic Chain ◽  
Parallel Manipulators ◽  
Type Synthesis ◽  
Displacement Analysis ◽  
Kinematic Chains ◽  
Small Joint ◽  
Actuated Joints

A method is proposed for the type synthesis of 3-DOF (degree-of-freedom) translational parallel manipulators (TPMs) based on screw theory. The wrench systems of a translational parallel kinematic chain (TPKC) and its legs are first analyzed. A general procedure is then proposed for the type synthesis of TPMs. The type synthesis of legs for TPKCs, the type synthesis of TPKCs as well as the selection of actuated joints of TPMs are dealt with in sequence. An approach to derive the full-cycle mobility conditions for legs for TPKCs is proposed based on screw theory and the displacement analysis of serial kinematic chains undergoing small joint motions. In addition to the TPKCs proposed in the literature, TPKCs with inactive joints are synthesized. The phenomenon of dependent joint groups in a TPKC is revealed systematically. The validity condition of actuated joints of TPMs is also proposed. Finally, linear TPMs, which are TPMs whose forward displacement analysis can be performed by solving a set of linear equations, are also revealed.

Synthesis of Two-Degree-of-Freedom Rotational Decoupled Manipulators of a 2R-Type Branch

2013 ◽  
Vol 284-287 ◽  
pp. 1929-1935
Author(s):  
Da Xing Zeng ◽  
Wen Juan Lu ◽  
Li Jie Zhang ◽  
Yi Tong Zhang
Keyword(s):  
Trajectory Planning ◽  
Screw Theory ◽  
Parallel Manipulators ◽  
Parallel Mechanisms ◽  
Type Synthesis ◽  
Precision Control ◽  
Kinematic Chains ◽  
Parallel Kinematic ◽  
Branch Type ◽  
Two Degree Of Freedom

Strong coupling is one of the prominent features of the general parallel mechanisms(Par. Mec.), which has led to difficulty in the trajectory planning and precision control. To solve this problem, the designing of motion decoupled parallel mechanisms(Dec. Par. Mec.) has become a hot topic. This paper, based on the work achieved in our pre-papers, is to make an improvement on the criterion for a branch type synthesis of the rotational decoupled parallel mechanisms(Rot. Dec. Par. Mec.), which ensures the decoupling of the rotations in each limb. This paper focuses on a type synthesis of the decoupled parallel mechanisms with two degree of freedoms (DOFs). Decoupled parallel manipulators with two parallel kinematic chains, one of which is of type 2R(R represents rotation), are taken into consideration in this paper. A large number of novel decoupled architectures are already obtained, some of which have got an application for a China Patent. What has been done in this paper is carried out by means of the screw theory, which has effectively avoided complex equations by synthesis.

scholarly journals Acceleration Analysis of 3DOF Parallel Manipulators

2013 ◽  
pp. 31-41
Author(s):  
Hassen Nigatu ◽  
Ajit Pal Singh ◽  
Solomon Seid
Keyword(s):  
Hessian Matrix ◽  
Parallel Manipulators ◽  
Unified Framework ◽  
Generalized Jacobian ◽  
New Approach ◽  
Kinematic Chains ◽  
Acceleration Analysis ◽  
Definition Of ◽  
Closure Constraints ◽  
Inverse Velocity

This paper presents a new approach to the velocity and acceleration analyses 3DOF parallel manipulators. Building on the definition of the ‘acceleration motor’, the forward and inverse velocity and acceleration equations are formulated such that the relevant analysis can be integrated under a unified framework that is based on the generalized Jacobian. A new Hessian matrix of serial kinematic chains (or limbs) is developed in an explicit and compact form using Lie brackets. This idea is then extended to cover parallel manipulators by considering the loop closure constraints. A 3- PRS parallel manipulator with coupled translational and rotational motion capabilities is analyzed to illustrate the generality and effectiveness of this approach.

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