Type Synthesis of Parallel Mechanisms With a Constant Jacobian Matrix

2018 ◽  
Vol 10 (6) ◽  
Author(s):  
Yanzhi Zhao ◽  
Yachao Cao ◽  
Xianwen Kong ◽  
Tieshi Zhao
Keyword(s):  
Jacobian Matrix ◽  
Screw Theory ◽  
Velocity Analysis ◽  
Parallel Mechanisms ◽  
Input Output ◽  
Type Synthesis ◽  
Analysis And Evaluation ◽  
Analysis Design ◽  
Moving Platform ◽  
And Control

Jacobian matrix plays a key role in the analysis, design, and control of robots. For example, it can be used for the performance analysis and evaluation of parallel mechanisms (PMs). However, the Jacobian matrix of a PM generally varies with the poses of the moving platform in the workspace. This leads to a nonconstant performance index of the PM. PMs with a constant Jacobian matrix have simple kinematics and are easy to design and control. This paper proposes a method for obtaining PMs with a constant Jacobian matrix. First, the criteria for detecting invariance of a Jacobian matrix are obtained based on the screw theory. An approach to the synthesis of PMs with a constant Jacobian matrix is then proposed. Using this approach, PMs with a constant Jacobian matrix are synthesized in two steps: the limb design and the combination of the limbs. Several PMs with a constant Jacobian matrix are obtained. In addition to the translational parallel mechanisms (TPMs) with a constant Jacobian matrix in the literature, the mixed-motion PMs whose moving platform can both translate and rotate with a constant Jacobian matrix are newly identified. The input/output velocity analysis of several PMs is presented to verify that Jacobian matrix of these PMs is constant.

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.

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.

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.

A New Index of Static Actuation Force Sensitivity of Mechanisms Based on Unified Forward Jacobian Matrix

2020 ◽  
Vol 12 (6) ◽  
Author(s):  
Xu Wang ◽  
Weizhong Guo ◽  
Youcheng Han
Keyword(s):  
Jacobian Matrix ◽  
Screw Theory ◽  
Structural Constraints ◽  
Parallel Mechanisms ◽  
Analysis Method ◽  
Actuation Force ◽  
Force Sensitivity ◽  
Differential Operation ◽  
Static Equation ◽  
Pose Optimization

Abstract This paper proposes a novel performance index, which is called static actuation force sensitivity (SAFS), to investigate the response of the actuation forces when the amplitude of the suffered load of the end-effector has a change. Smaller SAFS can protect the actuations, and the load is mainly suffered by the structural constraints. This work starts with the construction of the unified forward Jacobian matrix of both serial and parallel mechanisms by screw theory. Then, with the forward Jacobian matrix, the inverse static equation is established. SAFS is thus introduced by the “partial differential” operation on the inverse static equation. SAFS is only related to the position of the whole mechanism and the direction of the suffered load, but not related to the detailed value of the amplitude of the load and the detailed value of the actuation forces; thus, SAFS can reveal the essence of static force capacities of the mechanisms. The example mechanism (namely, the 3revolute-prismatic-spherical (RPS) parallel mechanism) is used to illustrate the distribution of SAFS both over the workspace and at a certain pose. The analysis method of SAFS and the proposed index are expected to be applied to the pose optimization in the motion planning of the mechanisms to protect the actuations.

Jacobian Derivation of 5-DOF 3R2T Parallel Mechanisms

2004 ◽  
Author(s):  
Qinchuan Li ◽  
Xudong Hu ◽  
Zhen Huang
Keyword(s):  
Degrees Of Freedom ◽  
Jacobian Matrix ◽  
Screw Theory ◽  
Kinematic Chain ◽  
Parallel Mechanisms ◽  
Mobility Analysis

This paper presents a method for the Jacobian derivation of 5-DOF 3R2T PMs (parallel mechanisms), where 3R denotes three rotational DOFs (degrees of freedom) and 2T denotes two translational DOFs. First the mobility analysis of such kind of parallel mechanisms is reviewed briefly. The Jacobian matrix of the single limb kinematic chain is obtained via screw theory, which is a 6 × 5 matrix. Then it is shown that the mobility analysis of such kind of PM is important when simplifying the 6 × 5 matrix into a 5 × 5 Jacobian matrix. After obtaining the 5 × 5 Jacobian matrix for each limb, a 5 × 5 Jacobian matrix for the whole mechanism can be established.

Type synthesis of 2R2T parallel mechanisms based on motion equivalent chain method

2014 ◽  
Vol 228 (17) ◽  
pp. 3209-3217 ◽  
Author(s):  
Wei Ye ◽  
Yuefa Fang ◽  
Sheng Guo ◽  
Haibo Qu
Keyword(s):  
Parallel Mechanism ◽  
Screw Theory ◽  
Parallel Mechanisms ◽  
Motion Pattern ◽  
Type Synthesis ◽  
Constraint Force ◽  
Single Loop ◽  
Loop Chain ◽  
Serial Chains

In this paper, the motion equivalent chain method is proposed and then applied to the type synthesis of a class of 2R2T parallel mechanism. The equivalent serial chains are synthesized for a specific 2R2T motion pattern based on screw theory. Feasible limb structures that provide a constraint couple and a constraint force are enumerated according to the reciprocity of the twist and wrench systems. Several motion equivalent single loop chains are constructed with the equivalent serial chains. Using motion equivalent single loop chains to replace the equivalent serial chains, a class of 2R2T parallel mechanisms is obtained based on the foundation of motion equivalent single loop chain structures.

Analysis on the Instantaneous Stiffness of the 3-RPS Parallel Machine

2009 ◽  
Vol 407-408 ◽  
pp. 63-67 ◽  
Author(s):  
Xian Guo Han ◽  
Xue Liang Cui ◽  
Wu Yi Chen
Keyword(s):  
Jacobian Matrix ◽  
Screw Theory ◽  
Parallel Machine ◽  
Force Analysis ◽  
Stiffness Model ◽  
Generalized Force ◽  
Moving Platform ◽  
Position And Orientation

Based on the screw theory, the force analysis of the 3-RPS parallel machine is illuminated. Been equivalent to a 6-chain parallel machine, the deformation harmony equation of the parallel machine under the outside generalized force is interpreted. The instantaneous stiffness model of the parallel machine, which includes the change of the force Jacobian matrix, is established. Considering the deviation of the position and orientation of the moving platform, which is resulted from the distortion of the PRS chains of the parallel machine, the influence of the change of the Jacobian matrix to the instantaneous stiffness model of the 3-RPS parallel machine is analyzed, and furthermore, it is verified with an instance.

Singularity Analysis of a Novel 4-DOFs Parallel Robot H4 by Using Screw Theory

2003 ◽  
Author(s):  
Hee-Byoung Choi ◽  
Atsushi Konno ◽  
Masaru Uchiyama
Keyword(s):  
Closed Loop ◽  
Jacobian Matrix ◽  
Screw Theory ◽  
Parallel Robot ◽  
Singularity Analysis ◽  
Loop Structure ◽  
Singular Configurations ◽  
Planning And Control ◽  
Kinematic Singularities ◽  
And Control

The closed-loop structure of a parallel robot results in complex kinematic singularities in the workspace. Singularity analysis become important in design, motion, planning, and control of parallel robot. The traditional method to determine a singular configurations is to find the determinant of the Jacobian matrix. However, the Jacobian matrix of a parallel manipulator is complex in general, and thus it is not easy to find the determinant of the Jacobian matrix. In this paper, we focus on the singularity analysis of a novel 4-DOFs parallel robot H4 based on screw theory. Two types singularities, i.e., the forward and inverse singularities, have been identified.

A 2(3-RRPS) parallel manipulator inspired by Gough–Stewart platform

Robotica ◽  
2012 ◽  
Vol 31 (3) ◽  
pp. 381-388 ◽  
Author(s):  
Jaime Gallardo-Alvarado ◽  
Mario A. García-Murillo ◽  
Eduardo Castillo-Castaneda
Keyword(s):  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Screw Theory ◽  
Parallel Manipulators ◽  
Forward Kinematics ◽  
Triangular Prism ◽  
Input Output ◽  
Six Degrees Of Freedom ◽  
Moving Platform

SUMMARYThis study addresses the kinematics of a six-degrees-of-freedom parallel manipulator whose moving platform is a regular triangular prism. The moving and fixed platforms are connected to each other by means of two identical parallel manipulators. Simple forward kinematics and reduced singular regions are the main benefits offered by the proposed parallel manipulator. The Input–Output equations of velocity and acceleration are systematically obtained by resorting to reciprocal-screw theory. A case study, which is verified with the aid of commercially available software, is included with the purpose to exemplify the application of the method of kinematic analysis.

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