Influence Coefficients and Singularity Analysis of a Novel 3-UPU Parallel Mechanism

2017 ◽  
Author(s):  
Ziming Chen ◽  
Dongliang Cheng ◽  
Yang Zhang ◽  
Zhiwei Yang ◽  
Jin Zhou
Keyword(s):  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Model Simulation ◽  
Hessian Matrix ◽  
Symmetry Plane ◽  
Coefficient Matrix ◽  
Singularity Analysis ◽  
Influence Coefficient ◽  
Parasitic Motion ◽  
Moving Platform

A novel 3-UPU parallel mechanism with two rotational and one translational (2R1T) degrees of freedom (DOFs) is analyzed in this paper. The base and moving platform of this mechanism are always symmetric about a middle symmetry plane. The moving platform can rotate continuously about any axis on the middle symmetry plane, so there exists no parasitic motion during the rotation. Using the kinematic influence coefficient theory and the imaginary mechanism method, the first and second order influence coefficient matrix (namely Jacobian matrix and Hessian matrix) of this mechanism are derived. The relations between the velocity and acceleration of the moving platform and the actuated links are obtained. In order to verify the correctness of the theory, two numerical examples are enumerated and varified by the 3D model simulation. The singularities of this mechanism is discussed and the singular configurations of the mechanism, including one kind of limb singularity and two kinds of platform singularities, are obtained.

Design and Analysis of 3-DOF Micromanipulator Driven by Piezoelectric Actuators

2008 ◽  
Author(s):  
Shihua Li ◽  
Yue Zhang ◽  
Zhen Huang ◽  
Changcheng Yu ◽  
Wenhua Ding
Keyword(s):  
Finite Element ◽  
Finite Element Modeling ◽  
Parallel Mechanism ◽  
Piezoelectric Actuators ◽  
Coefficient Matrix ◽  
Influence Coefficient ◽  
Velocity Analysis ◽  
First Order ◽  
Flexure Hinges ◽  
Moving Platform

A novel 3-DOF parallel micromanipulator which is driven by piezoelectric actuators has been developed that based on 3–5R parallel mechanism. The micromanipulator consists of a moving platform, a fixed platform, three 5R fixed-length chains and three piezoelectric actuators. In this paper, the first-order influence coefficient matrix of the micromanipulator is given, and then the velocity analysis is given. The dimension of the platform and flexure hinges and the position of flexure are designed, and the safety check of the flexible hinges and the designed mechanism is done with the aid of finite element modeling to provide good stiffness with little bending deformation of the platform. The merits of parallel mechanism and piezoelectric actuators are reflected in this mechanism.

Stiffness and singularity analysis of foldable parallel mechanism for ship-based stabilized platform

Robotica ◽  
2014 ◽  
Vol 34 (4) ◽  
pp. 913-924 ◽  
Author(s):  
Tie-shi Zhao ◽  
Chang Wang ◽  
Xiao Liu ◽  
Hui Bian ◽  
Yan-zhi Zhao
Keyword(s):  
Stiffness Matrix ◽  
Parallel Mechanism ◽  
Singularity Analysis ◽  
Degree Of Freedom ◽  
Influence Coefficient ◽  
Rotational Stiffness ◽  
Closed Chain ◽  
Moving Platform ◽  
Stabilized Platform ◽  
Directional Stiffness

SUMMARYThis paper investigates a 6-degree-of-freedom foldable parallel mechanism for the ship-based stabilized platform, which is driven by closed chain linkages. The velocity and acceleration mappings between the moving platform and inputs of the closed chain linkages are deduced in the form of the first- and second-order influence coefficient matrices. The continuous stiffness matrix is deduced; furthermore, the translation and rotational stiffness along any direction are also deduced. With directional stiffness, the singularity of the mechanism is analyzed, and the explanation of the singularity is given from the viewpoint of stiffness. The directions the platform cannot move or lose its constraints are got from directional stiffness.

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.

Motion Characteristics Analysis of a Novel 2R1T 3-UPU Parallel Mechanism

2019 ◽  
Vol 142 (1) ◽  
Author(s):  
Chen Zhao ◽  
Ziming Chen ◽  
Yanwen Li ◽  
Zhen Huang
Keyword(s):  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Control Method ◽  
Speed Control ◽  
Singularity Analysis ◽  
Mobile Platform ◽  
Rotational Axis ◽  
Constraint Forces ◽  
Parasitic Motion ◽  
Motion Characteristics

Abstract In this paper, a novel 3-UPU (P and U stand for prismatic and universal joints, respectively) parallel mechanism (PM) and its variant PM are proposed. Both of them have two rotational and one translational (2R1T) degrees of freedom (DOFs) without involving any parasitic motion. Mobility analysis shows that the three constraint forces provided by three limbs of the mechanism are located on the same plane and the mobile platform can translate perpendicular to this plane and rotate around any axis on it. Analysis of the mechanism’s motion characteristics demonstrates that the mobile platform outputs either pure rotation or pure translation. Moreover, the rotational axis can be fixed during the rotation process, which means no parasitic motion is involved. The causes of the motion characteristics are analyzed by the combination of an overall Jacobian matrix, a statistical method, and a geometric method. The PMs only need to translate or rotate once to move from the initial configuration to the final configuration, which allows for easy control of speeds. The relationship between mechanism parameters and singularity is analyzed. A speed control method for the PMs is proposed and a prototype is designed and made. Experiments are conducted to verify the determined motion characteristics, the speed control method, and the singularity analysis.

scholarly journals Optimum Seeking of Redundant Actuators for M-RCM 3-UPU Parallel Mechanism

2020 ◽  
Author(s):  
Chen Zhao ◽  
Jingke Song ◽  
Xuechan Chen ◽  
Ziming Chen ◽  
Huafeng Ding
Keyword(s):  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Singularity Analysis ◽  
Universal Joint ◽  
Prismatic Joint ◽  
Transmission Index ◽  
Redundant Actuators ◽  
Force Transmissibility ◽  
Singular Configuration

Abstract This paper focuses on a 2R1T 3-UPU (U for universal joint and P for prismatic joint) parallel mechanism (PM) with two rotational and one translational (2R1T) degrees of freedom (DOFs) and the ability of multiple remote centers of motion (M-RCM). The singularity analysis based on the indexes of motion/force transmissibility and constraint shows that this PM has transmission singularity, constraint singularity, mixed singularity and limb singularity. To solve these singularproblems, the quantifiable redundancy transmission index (RTI) and the redundancy constraint index (RCI) are proposed for optimum seeking of redundant actuators for this PM. Then the appropriate redundant actuators are selected and the working scheme for redundant actuators near the corresponding singular configuration are given to help the PM go through the singularity.

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.

Acceleration and Dexterity Performance Indices for 6-DOF and Lower-Mobility Parallel Mechanism

2004 ◽  
Author(s):  
X. J. Guo ◽  
F. Q. Chang ◽  
S. J. Zhu
Keyword(s):  
Parallel Mechanism ◽  
Robot Manipulator ◽  
Coefficient Matrix ◽  
Second Order ◽  
Influence Coefficient ◽  
Global Index ◽  
Performance Indices ◽  
First Order ◽  
Lower Mobility

On the basis of first-order and second-order kinematic influence coefficient matrices, dynamics characteristics indices for robot manipulator are presented in the paper. Different from indices before, these indices include not only the first-order kinematics influence coefficient matrix G, but also the second-order kinematic influence coefficient matrix H. Then with the global index, these indices can be used to guide the dynamics design.

Kinematics of a Pure Translational UPS/3RPaPaR Parallel Mechanism

2007 ◽  
Author(s):  
Chung-Ching Lee ◽  
Po-Chih Lee
Keyword(s):  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Translational Motion ◽  
Singularity Analysis ◽  
Inverse Kinematic ◽  
Geometric Constraints ◽  
Design Parameters ◽  
Numerical Illustration ◽  
The Matrix ◽  
Kinematic Analyses

From the viewpoint of kinematics, a type of 3 degrees of freedom (dofs) UPS/3RPaPaR overconstrained parallel mechanism (Pa means the hinged 4R parallelogram) with pure translational motion is presented for the development of automatic assembly devices or as a regional structure in the hybrid parallel platform. In the beginning, the formation & mobility are elucidated and the 4×4 transformation matrix & the D-H notation with specific geometric constraints verify the pure translational motion. The forward and inverse kinematic analyses are then established in the analytical closed-form through the matrix method. Besides, we take a numerical illustration for the confirmation of correctness of the derived equations. The determination of workspace is also attained by the intersection of volumes swept by each limb. In addition, the Jacobian matrix and its condition number indicated by Euclidean norm as a function of design parameters are further achieved. Finally, the singularity analysis of the configuration based on the direct and inverse kinematic J-matrix during the movement is identified in detail.

Controllable Rotation Workspace of a Metamorphic Parallel Mechanism With Reconfigurable Universal Joints

2013 ◽  
Author(s):  
Dongming Gan ◽  
Jian S. Dai ◽  
Jorge Dias ◽  
Lakmal D. Seneviratne
Keyword(s):  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Jacobian Matrix ◽  
Central Line ◽  
Singularity Analysis ◽  
Euler Angles ◽  
Base Plane ◽  
Constraint Forces ◽  
Joint Rotation ◽  
Universal Joints

This paper introduces a metamorphic parallel mechanism which has three topologies with pure translational, pure rotational and 3T1R degrees of freedom. Mobility change stemming from the reconfigurability of a reconfigurable Hooke (rT) joint is illustrated by change of the limb twist screw systems and the platform constraint screw system. Then the paper focuses on the pure rotational topology of the mechanism of which the rotational center can be altered along the central line perpendicular to the base plane by altering the radial rotational axes in the limbs. Singularity analysis is conducted based on the dependency of constraint forces and actuation forces in a screw based Jacobian matrix. Following these, rotation workspace variation is demonstrated in a 2D projection format using the Tilt-and-Torsion Euler angles based on the actuation limits and joint rotation ranges.

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