Block Adjacency Matrix Method for Analyzing the Configuration Transformations of Metamorphic Parallel Mechanisms

2014 ◽  
Author(s):  
Duanling Li ◽  
Chunxia Li ◽  
Zhonghai Zhang ◽  
Xianwen Kong
Keyword(s):  
Adjacency Matrix ◽  
Matrix Method ◽  
Parallel Mechanism ◽  
New Method ◽  
Parallel Mechanisms ◽  
Adjacency Matrices ◽  
Moving Platform ◽  
Internal Configuration ◽  
Spherical Motion ◽  
Metamorphic Mechanisms

Metamorphic transformation is a fundamental and key issue in the design and analysis of metamorphic mechanisms. It is tedious to represent and calculate the metamorphic transformations of metamorphic parallel mechanisms using the existing adjacency matrix method. To simplify the configuration transformation analysis, we propose a new method based on block adjacency matrix to analyze the configuration transformations of metamorphic parallel mechanisms. A block adjacency matrix is composed of three types of elements, including limb matrices that are adjacency matrices each representing a limb of a metamorphic parallel mechanism, row matrices each representing how a limb is connected to the moving platform, and column matrices each representing how a limb is connected to the base. Manipulations of the block adjacency matrix for analyzing the metamorphic transformations are presented systematically. If only the internal configuration of a limb changes, the configuration transformations can be obtained by simply calculating the corresponding limb matrix. A 3-URRRR metamorphic parallel mechanism, which has five configurations including a 1-DOF translation configuration and a 3-DOF spherical motion configuration, is taken as an example to illustrate the effectiveness of the proposed approach to the metamorphic transformation analysis of metamorphic parallel mechanism.

scholarly journals Reconfiguration Analysis of a 3-DOF Parallel Mechanism

Robotics ◽  
2019 ◽  
Vol 8 (3) ◽  
pp. 66
Author(s):  
Maurizio Ruggiu ◽  
Xianwen Kong
Keyword(s):  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Operation Mode ◽  
Parallel Mechanisms ◽  
Universal Joint ◽  
Kinematic Chains ◽  
Constraint Equations ◽  
The Third ◽  
Equilateral Triangles ◽  
Moving Platform

This paper deals with the reconfiguration analysis of a 3-DOF (degrees-of-freedom) parallel manipulator (PM) which belongs to the cylindrical parallel mechanisms family. The PM is composed of a base and a moving platform shaped as equilateral triangles connected by three serial kinematic chains (legs). Two legs are composed of two universal (U) joints connected by a prismatic (P) joint. The third leg is composed of a revolute (R) joint connected to the base, a prismatic joint and universal joint in sequence. A set of constraint equations of the 1-RPU−2-UPU PM is derived and solved in terms of the Euler parameter quaternion (a.k.a. Euler-Rodrigues quaternion) representing the orientation of the moving platform and of the Cartesian coordinates of the reference point on the moving platform. It is found that the PM may undergo either the 3-DOF PPR or the 3-DOF planar operation mode only when the base and the moving platform are identical. The transition configuration between the operation modes is also identified.

Type Synthesis of Parallel Mechanisms With Multiple Operation Modes

2006 ◽  
Author(s):  
Xianwen Kong ◽  
Cle´ment M. Gosselin ◽  
Pierre-Luc Richard
Keyword(s):  
Parallel Mechanism ◽  
Translational Motion ◽  
Parallel Mechanisms ◽  
Motion Pattern ◽  
Type Synthesis ◽  
Motion Patterns ◽  
Operation Modes ◽  
Multiple Operation ◽  
Spherical Motion ◽  
General Method

There are usually several motion patterns having the same DOF (degree of freedom). For example, planar motion, spherical motion, and spatial translation are motion patterns with 3-DOF. An f-DOF parallel mechanism with multiple operation modes is a parallel mechanism that can generate different motion patterns with f DOF. Up to now, no method has been proposed for the type synthesis of parallel mechanisms with multiple operation modes. This paper presents a general method for the type synthesis of parallel mechanisms with multiple operation modes. Using the proposed approach, 3-DOF parallel mechanisms with both spherical and translational modes, i.e., parallel mechanisms generating both the spherical motion pattern and the spatial translational motion pattern, are generated systematically. A large number of parallel mechanisms with both spherical and translational modes are obtained.

Application of Parallel Mechanism in Multi-DIM Vibration Absorbers

2014 ◽  
Vol 532 ◽  
pp. 297-300 ◽  
Author(s):  
Chang Chun Yu
Keyword(s):  
Parallel Mechanism ◽  
Simple Structure ◽  
High Accuracy ◽  
New Method ◽  
Vibration Absorber ◽  
Vibration Absorbers ◽  
Parallel Mechanisms ◽  
Vibration Absorption ◽  
Absorption Field ◽  
Compact Mechanism

It introduces ways and means of designing this kind of vibration absorbers which are presented using parallel mechanisms as the main mechanisms ,it ,which takes the parallel mechanisms with 3-DOF translation as an example, validates the feasibility of the method, and enumerates some of the parallel mechanisms that are fit for multi-DIM vibration absorber. In a word, the multi-DIM vibration absorber system based on parallel mechanism is a new idea and breakthrough in multi-DIM vibration absorption field, which has the characteristic of simple structure, compact mechanism, high accuracy, partially or fully decoupled mechanism easy for control and so on, and provides a new method for the study of Multi-DIM vibration.

scholarly journals A holographic matrix representation of the metamorphic parallel mechanisms

2019 ◽  
Vol 10 (2) ◽  
pp. 437-447
Author(s):  
Wei Sun ◽  
Jianyi Kong ◽  
Liangbo Sun
Keyword(s):  
Adjacency Matrix ◽  
Topological Structure ◽  
Incidence Matrix ◽  
Matrix Representation ◽  
Evolutionary Relationships ◽  
Parallel Mechanisms ◽  
Metamorphic Mechanism ◽  
The Matrix ◽  
Metamorphic Mechanisms

Abstract. Metamorphic mechanisms belong to the class of mechanisms that are able to change their configurations sequentially to meet different requirements. In this paper, a holographic matrix representation for describing the topological structure of metamorphic mechanisms was proposed. The matrix includes the adjacency matrix, incidence matrix, links attribute and kinematic pairs attribute. Then, the expanded holographic matrix is introduced, which includes driving link, frame link and the identifier of the configurations. Furthermore, a matrix representation of an original metamorphic mechanism is proposed, which has the ability to evolve into various sub-configurations. And evolutionary relationships between mechanisms in sub-configurations and the original metamorphic mechanism are determined distinctly. Examples are provided to demonstrate the validation 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.

Classification of 3-DOF 3-UPU Translational Parallel Mechanisms Based on Constraint Singularity Loci Using Gröbner Cover

2021 ◽  
Author(s):  
Xianwen Kong
Keyword(s):  
Parallel Mechanism ◽  
Polynomial Systems ◽  
Coordinate Frame ◽  
Parallel Mechanisms ◽  
Systematic Classification ◽  
Starting Point ◽  
Moving Platform ◽  
Singular Configuration ◽  
The Impact

Abstract A 3-UPU translational parallel mechanism (TPM) is one of typical TPMs. Several types of 3-UPU TPMs have been proposed in the literature. Despite comprehensive studies on 3-UPU TPMs in which the joint axes on the base and the moving platform are coplanar, only a few 3-UPU TPMs with a skewed base and moving platform have been proposed. However, the impact of link parameters on singularity loci of such TPMs has not been systematically investigated. The advances in computing CGS (comprehensive Gröbner system) or Gröbner cover of parametric polynomial systems provide an efficient tool for solving this problem. This paper presents a systematic classification of 3-UPU TPMs, especially those with a skewed base and moving platform, based on constraint singularity loci. First, the constraint singularity equation of a 3-UPU TPM is derived. To simplify this equation, the coordinate frame on the base (or moving platform) is set up such that the centers of three U joints are located on different coordinate axes. Using Gröbner Cover, the 3-UPU TPMs are classified into 20 types based on the constraint singularity loci. Finally, a novel 3-UPU TPM is proposed. Unlike most of existing 3-UPU TPMs which can transit to two or more 3-DOF operation modes at a constraint singular configuration, the proposed 3-UPU TPM can only transit to one general 3-DOF operation mode in a constraint singular configuration. The singularity locus divides the workspace of this 3-UPU TPM into two constraint singularity-free regions. This work provides a solid foundation for the design of 3-UPU TPMs and a starting point for the classification of a general 3-UPU parallel mechanism.

Study on Structural Error Compensation of 3-UPU Parallel Mechanism

2020 ◽  
Vol 13 (8) ◽  
pp. 1266-1274
Author(s):  
Yonggeng Wei ◽  
Xin Shi ◽  
Zhongxian Wang
Keyword(s):  
Error Compensation ◽  
Parallel Mechanism ◽  
Least Squares Method ◽  
Numerical Control ◽  
Parallel Mechanisms ◽  
Connecting Rod ◽  
Position Change ◽  
Positioning Accuracy ◽  
Solution Equation ◽  
Moving Platform

Background: Compared with the traditional series mechanism, the parallel mechanism has a better kinematic performance. Structural size error is the main factor affecting the accuracy of parallel mechanisms. Objective: The paper mainly studies the compensation of the rod length error, the moving platform radius error and the fixed platform radius error of 3-UPU parallel mechanism. Methods: To establish a generalized forward and inverse solution equation with error compensation, the position change of the moving platform is measured by a laser interferometer, and the change amount of the three connecting rod lengths at the corresponding position is recorded. Optimized by least squares method, the optimized error compensation values are compensated to the kinematics algorithm of the numerical control system, and the positioning accuracy is improved. Results: The results show that the positioning accuracy is higher when the mechanism moves in the lower plane, and the positioning error in the z axis direction is smaller than x, y, y=x, y=-x axis. Conclusion: After the error compensation, the overall positioning accuracy of the mechanism is increased by 60%.

A serial of novel four degrees of freedom parallel mechanisms with large rotational workspace

Robotica ◽  
2014 ◽  
Vol 34 (4) ◽  
pp. 764-776 ◽  
Author(s):  
Sheng Guo ◽  
Wei Ye ◽  
Haibo Qu ◽  
Dan Zhang ◽  
Yuefa Fang
Keyword(s):  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Screw Theory ◽  
Planetary Gear ◽  
Gear Train ◽  
Parallel Mechanisms ◽  
Kinematics Analysis ◽  
Kinematic Chains ◽  
Moving Platform ◽  
Partition Method

SUMMARYIn this paper, a class of novel four Degrees of Freedom (DOF) non-overconstrained parallel mechanisms with large rotational workspace is presented based on screw theory. First, the conflict between the number of independent constraints applied on the moving platform and the number of kinematic limbs for 4-DOF non-overconstrained parallel mechanism is identified. To solve this conflict, the platform partition method is introduced, and two secondary platforms are employed in each of the parallel mechanisms. Then, the motion requirements of the secondary platforms are analyzed and all the possible kinematic chains are enumerated. The geometrical assembly conditions of all possible secondary limbs are analyzed and some typical non-overconstrained parallel mechanisms are generated. In each of the parallel mechanisms, a planetary gear train is used to connect both of the secondary platforms. The large rotational workspace of the moving platform is obtained due to the relative motion of the two secondary platforms. Finally, the kinematics analysis of a typical parallel mechanism is conducted.

scholarly journals Topological and Kinematic Singularities for a Class of Parallel Mechanisms

2009 ◽  
Vol 2009 ◽  
pp. 1-12 ◽  
Author(s):  
Nir Shvalb ◽  
Moshe Shoham ◽  
Hagay Bamberger ◽  
David Blanc
Keyword(s):  
Parallel Mechanism ◽  
Necessary Condition ◽  
Parallel Mechanisms ◽  
Kinematic Singularity ◽  
Planar Case ◽  
Moving Platform ◽  
Kinematic Singularities

We study singularities for a parallel mechanism with a planar moving platform in , with joints which are universal, spherical (spatial case), or rotational (planar case). For such mechanisms, we give a necessary condition for a topological singularity to occur, and describe the corresponding kinematic singularity. An example is provided.

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.

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