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.

A Systematical Approach for Structure Synthesis of Parallel Mechanisms Based on Single-Open-Chain Modules and Its Application

2009 ◽  
Author(s):  
Ting-Li Yang ◽  
An-Xin Liu ◽  
Qiong Jin ◽  
Yu-Feng Luo ◽  
Lu-Bin Hang ◽  
...  
Keyword(s):  
Parallel Mechanism ◽  
Systematic Approach ◽  
Screw Theory ◽  
Parallel Mechanisms ◽  
Type Synthesis ◽  
Open Chain ◽  
Structure Synthesis ◽  
Vector Algebra ◽  
Algebra Theory ◽  
Position And Orientation

Based on previous research results presented by authors, this paper proposes a novel systematic approach for structure synthesis of all parallel mechanisms (excluding Bennett mechanism etc), which is totally different from the approaches based on screw theory and based on displacement subgroup. Main characteristics of this approach are: (a) the synthesized mechanisms are non-instantaneous ones, and (b) only simple mathematical tools (vector algebra, theory of sets, etc.) are used. Main steps of this approach include: (1) Determining functional and structural requirements of the parallel mechanism to be synthesized, such as position and orientation characteristic (POC) matrix, degree of freedom (DOF), etc. (2) Type synthesis of branches. (3) Assembling of branches (determining the geometry constraint conditions among the branches attached between the moving platform and the frame, and checking the DOF). (4) Identifying the inactive joints. (5) Selecting the actuating joints. In order to illustrate the whole procedure, the type synthesis of spherical parallel mechanisms is studied using this approach.

Singularity Analysis of Large Workspace 3RRRS Parallel Mechanism Using Line Geometry and Linear Complex Approximation

2010 ◽  
Vol 3 (1) ◽  
Author(s):  
Alon Wolf ◽  
Daniel Glozman
Keyword(s):  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Screw Theory ◽  
Singularity Analysis ◽  
Community Research ◽  
Parallel Mechanisms ◽  
Line Geometry ◽  
Equilibrium Equations ◽  
Six Degrees Of Freedom ◽  
Singular Configurations

During the last 15 years, parallel mechanisms (robots) have become more and more popular among the robotics and mechanism community. Research done in this field revealed the significant advantage of these mechanisms for several specific tasks, such as those that require high rigidity, low inertia of the mechanism, and/or high accuracy. Consequently, parallel mechanisms have been widely investigated in the last few years. There are tens of proposed structures for parallel mechanisms, with some capable of six degrees of freedom and some less (normally three degrees of freedom). One of the major drawbacks of parallel mechanisms is their relatively limited workspace and their behavior near or at singular configurations. In this paper, we analyze the kinematics of a new architecture for a six degrees of freedom parallel mechanism composed of three identical kinematic limbs: revolute-revolute-revolute-spherical. We solve the inverse and show the forward kinematics of the mechanism and then use the screw theory to develop the Jacobian matrix of the manipulator. We demonstrate how to use screw and line geometry tools for the singularity analysis of the mechanism. Both Jacobian matrices developed by using screw theory and static equilibrium equations are similar. Forward and inverse kinematic solutions are given and solved, and the singularity map of the mechanism was generated. We then demonstrate and analyze three representative singular configurations of the mechanism. Finally, we generate the singularity-free workspace of the mechanism.

The Effects of Actuation Schemes on the Kinematic Performance of Manipulators

1997 ◽  
Vol 119 (2) ◽  
pp. 212-217 ◽  
Author(s):  
R. Matone ◽  
B. Roth
Keyword(s):  
Performance Measures ◽  
Condition Number ◽  
Jacobian Matrix ◽  
Kinematic Model ◽  
Joint Space ◽  
Singular Value ◽  
End Effector ◽  
Kinematic Performance ◽  
Actuation Scheme ◽  
Space Description

This paper is concerned with the effects of actuation schemes on three measures of kinematic performance which depend upon a manipulator’s Jacobian matrix (namely, the minimum singular value, the manipulability, and the condition number). We begin by presenting a simple framework on how to incorporate actuator location and drive mechanisms in the kinematic model. Then, we redefine the performance measures using the new model. For each measure we derive properties relating its joint space to its actuator space description. Next we demonstrate that the choice of actuation scheme influences the size, shape, and direction of the velocity ellipsoid of the end-effector. Finally, we employ the above concepts in the design of a 2R planar mechanical arm. Its transmission ratios and drive mechanisms are selected in order to obtain good kinematic characteristics. We show that the choice of actuation scheme can be used to improve kinematic performance.

Mobility Analysis of Parallel Mechanisms Based on Screw Theory and the Concept of Equivalent Serial Kinematic Chain

2005 ◽  
Author(s):  
Xianwen Kong ◽  
Cle´ment M. Gosselin
Keyword(s):  
Systematic Approach ◽  
Screw Theory ◽  
Kinematic Chain ◽  
Second Step ◽  
Parallel Mechanisms ◽  
Mobility Analysis ◽  
Single Loop ◽  
Kinematic Chains ◽  
Serial Chain ◽  
Parallel Kinematic

This paper presents a systematic approach for the mobility analysis of parallel mechanisms. The method is based on screw theory and the concept of equivalent serial chain. An equivalent serial kinematic chain of a k-legged PKC (parallel kinematic chain) is defined as a serial kinematic chain which has the same twist system and the wrench system as the k-legged PKC. Using the proposed approach, the mobility analysis of a PKC is performed in two steps. The first step is the instantaneous mobility analysis, and the second step is the full-cycle mobility inspection. The first step is dealt with based on screw theory. The second step is performed with the aid of the concept of equivalent serial chain and the types of multi-DOF overconstrained single-loop kinematic chains. The proposed approach is illustrated with several examples.

Singularity Analysis of 3-DOF Planar Parallel Mechanisms via Screw Theory

2003 ◽  
Vol 125 (3) ◽  
pp. 573-581 ◽  
Author(s):  
Ilian A. Bonev ◽  
Dimiter Zlatanov ◽  
Cle´ment M. Gosselin
Keyword(s):  
Screw Theory ◽  
Singularity Analysis ◽  
Point Of View ◽  
Mobile Platform ◽  
Parallel Mechanisms ◽  
Singular Configurations ◽  
Revolute Joints ◽  
Singular Configuration

This paper presents the results of a detailed study of the singular configurations of 3-DOF planar parallel mechanisms with three identical legs. Only prismatic and revolute joints are considered. From the point of view of singularity analysis, there are ten different architectures. All of them are examined in a compact and systematic manner using planar screw theory. The nature of each possible singular configuration is discussed and the singularity loci for a constant orientation of the mobile platform are obtained. For some architectures, simplified designs with easy to determine singularities are identified.

Structure Synthesis of Rank-Degenerated Serial Mechanisms and Over-Constrained Single-Loop Kinematic Chains

2009 ◽  
Author(s):  
Ting-Li Yang ◽  
An-Xin Liu ◽  
Qiong Jin ◽  
Yu-Feng Luo ◽  
Hui-Ping Shen ◽  
...  
Keyword(s):  
Systematic Approach ◽  
Screw Theory ◽  
Degree Of Freedom ◽  
Parallel Mechanisms ◽  
Single Loop ◽  
Kinematic Chains ◽  
Structure Synthesis ◽  
Vector Algebra ◽  
Position And Orientation

Based on the Position and orientation characteristic (POC) equation of serial mechanisms proposed by the author, this paper presents a novel systematic approach for structure synthesis of rank-degenerated serial mechanisms and over-constrained single-loop kinematic chains (KCs) (excluding the Bennett mechanism etc). This approach is totally different from the approaches based on the screw theory and based on the displacement subgroup, and only simple mathematical tools (vector algebra, etc.) are used. Using this approach, the structure types of serial mechanisms with the specified ranks and the specified degree of freedom (DOF) are synthesized firstly. After that, using the structure types of the obtained serial mechanisms, structure types of over-constrained single-loop KCs with the specified ranks and the specified DOF can be generated in a straightforward way. The structure types of the obtained serial mechanisms can be used as branches of parallel mechanisms. The structure types and the ranks of the obtained over-constrained single-loop KCs can be used to calculate the DOF of multi-loop mechanisms. In fact, the systematic approach proposed in this paper is a key component of the systematic approach for structure synthesis of parallel mechanisms.

The Effects of Actuation Schemes on the Kinematic Performance of Manipulators

1996 ◽  
Author(s):  
Ricardo Matone ◽  
Bernard Roth
Keyword(s):  
Performance Measures ◽  
Condition Number ◽  
Jacobian Matrix ◽  
Kinematic Model ◽  
Joint Space ◽  
Singular Value ◽  
End Effector ◽  
Kinematic Performance ◽  
Actuation Scheme ◽  
Space Description

Abstract This paper is concerned with the effects of actuation schemes on three measures of kinematic performance which depend upon a manipulator’s Jacobian matrix (namely, the minimum singular value, the manipulability, and the condition number.) We begin by presenting a simple framework on how to incorporate actuator location and drive mechanisms in the kinematic model. Then, we redefine the performance measures using the new model. For each measure we derive properties relating its joint space to its actuator space description. Next we demonstrate that the choice of actuation scheme influences the size, shape, and direction of the velocity ellipsoid of the end-effector. Finally, we employ the above concepts in the design of a 2R planar mechanical arm. Its transmission ratios and drive mechanisms are selected in order to obtain good kinematic characteristics. We show that the choice of actuation scheme can be used to improve kinematic performance.

Singularity Loci of a Special Class of Spherical 3-DOF Parallel Mechanisms With Prismatic Actuators

2004 ◽  
Vol 126 (2) ◽  
pp. 319-326 ◽  
Author(s):  
Jing Wang ◽  
Cle´ment M. Gosselin
Keyword(s):  
Special Class ◽  
Three Dimensional ◽  
Parallel Manipulators ◽  
Joint Space ◽  
Parallel Mechanisms ◽  
Singular Configurations ◽  
Planning And Control ◽  
Robot Trajectory ◽  
Special Cases ◽  
And Control

In this paper, the singularity loci of a special class of spherical 3-DOF parallel manipulators with prismatic actuators are studied. Concise analytical expressions describing the singularity loci are obtained in the joint and in the Cartesian spaces by using the expression of the determinant of the Jacobian matrix and the inverse kinematics of the manipulators. It is well known that there exist three different types of singularities for parallel manipulators, each having a different physical interpretation. In general, the singularity of type II is located inside the Cartesian workspace and leads to the instability of the end-effector. Therefore, it is important to be able to identify the configurations associated with this type of singularity and to find their locus in the space of all configurations. For the class of manipulators studied here, the six general cases and the five special cases of singularities are discussed. It is shown that the singularity loci in the Cartesian space (defined by the three Euler angles) are six independent planes. In the joint space (defined by the length of the three input links), the singularity loci are quadric surfaces, such as hyperboloid, sphere or a degenerated line or a degenerated circle. In addition, the three-dimensional graphical representations of the singular configurations in each of the general and special cases are illustrated. The description of the singular configurations provided here has great significance for robot trajectory planning and control.

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.

scholarly journals A New Method for Type Synthesis of 2R1T and 2T1R 3-DOF Redundant Actuated Parallel Mechanisms with Closed Loop Units

2020 ◽  
Vol 33 (1) ◽  
Author(s):  
Yongquan Li ◽  
Yang Zhang ◽  
Lijie Zhang
Keyword(s):  
Closed Loop ◽  
Screw Theory ◽  
Line Graph ◽  
Degree Of Freedom ◽  
Parallel Mechanisms ◽  
Type Synthesis ◽  
Allocation Criteria ◽  
Grassmann Line Geometry ◽  
Moving Platform ◽  
Atlas Method

Abstract The current type synthesis of the redundant actuated parallel mechanisms is adding active-actuated kinematic branches on the basis of the traditional parallel mechanisms, or using screw theory to perform multiple getting intersection and union to complete type synthesis. The number of redundant parallel mechanisms obtained by these two methods is limited. In this paper, based on Grassmann line geometry and Atlas method, a novel and effective method for type synthesis of redundant actuated parallel mechanisms (PMs) with closed-loop units is proposed. Firstly, the degree of freedom (DOF) and constraint line graph of the moving platform are determined successively, and redundant lines are added in constraint line graph to obtain the redundant constraint line graph and their equivalent line graph, and a branch constraint allocation scheme is formulated based on the allocation criteria. Secondly, a scheme is selected and redundant lines are added in the branch chains DOF graph to construct the redundant actuated branch chains with closed-loop units. Finally, the branch chains that meet the requirements of branch chains configuration criteria and F&C (degree of freedom & constraint) line graph are assembled. In this paper, two types of 2 rotational and 1 translational (2R1T) redundant actuated parallel mechanisms and one type of 2 translational and 1 rotational (2T1R) redundant actuated parallel mechanisms with few branches and closed-loop units were taken as examples, and 238, 92 and 15 new configurations were synthesized. All the mechanisms contain closed-loop units, and the mechanisms and the actuators both have good symmetry. Therefore, all the mechanisms have excellent comprehensive performance, in which the two rotational DOFs of the moving platform of 2R1T redundant actuated parallel mechanism can be independently controlled. The instantaneous analysis shows that all mechanisms are not instantaneous, which proves the feasibility and practicability of the method.

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