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

2021 ◽  
Vol 34 (1) ◽  
Author(s):  
Chen Zhao ◽  
Jingke Song ◽  
Xuechan Chen ◽  
Ziming Chen ◽  
Huafeng Ding
Keyword(s):  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Singularity Analysis ◽  
Quantitative Criterion ◽  
Singularity Problem ◽  
Transmission Index ◽  
Redundant Actuators ◽  
Open Issue ◽  
Force Transmissibility ◽  
Singular Configuration

AbstractThe singularity problem brings troubles to the design and application for the parallel mechanism. Currently, redundant actuation is one of the useful methods to solve this singularity problem. However, faced to the numerous joints in a parallel mechanism, how to make a quantitative criterion of seeking the most efficient joints added actuators for letting the mechanism passes through singularity is a necessarily open issue. 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 singular problems, 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 passes through the singularity. This research proposes a quantitative criterion to optimum seeking of redundant actuators for the parallel mechanism to solve its singularity.

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.

Singularity Analysis of Serial Robot-Manipulators

1996 ◽  
Vol 118 (4) ◽  
pp. 520-525 ◽  
Author(s):  
A. Karger
Keyword(s):  
Degrees Of Freedom ◽  
Robot Manipulator ◽  
Robot Manipulators ◽  
Singularity Analysis ◽  
Singular Set ◽  
Singular Configurations ◽  
Special Cases ◽  
Serial Robot ◽  
Singular Configuration ◽  
Actual Configuration

This paper is devoted to the description of the set of all singular configurations of serial robot-manipulators. For 6 degrees of freedom serial robot-manipulators we have developed a theory which allows to describe higher order singularities. By using Lie algebra properties of the screw space we give an algorithm, which determines the degree of a singularity from the knowledge of the actual configuration of axes of the robot-manipulator only. The local shape of the singular set in a neighbourhood of a singular configuration can be determined as well. We also solve the problem of escapement from a singular configuration. For serial robot-manipulators with the number of degrees of freedom different from six we show that up to certain exceptions singular configurations can be avoided by a small change of the motion of the end-effector. We also give an algorithm which allows to determine equations of the singular set for any serial robot-manipulator. We discuss some special cases and give examples of singular sets including PUMA 560.

New Indices for Optimal Design of Redundantly Actuated Parallel Manipulators

2016 ◽  
Vol 9 (1) ◽  
Author(s):  
Qinchuan Li ◽  
Ningbin Zhang ◽  
Feibo Wang
Keyword(s):  
Optimal Design ◽  
Degrees Of Freedom ◽  
Parallel Manipulators ◽  
Mean Value ◽  
Transmission Performance ◽  
Transmission Index ◽  
Redundantly Actuated ◽  
Lower Mobility ◽  
Six Dof ◽  
Force Transmissibility

Redundantly actuated parallel manipulators (PMs) receive growing interest due to their reduced singularity and enlarged workspace. This paper proposes new indices for optimal design and analysis of redundantly actuated PMs by evaluating their motion/force transmissibility. First, we proposed a method to extract a multi-DOF (degrees-of-freedom) redundantly actuated PM into several subsidiary one-DOF PMs with two or more actuators by locking some actuators in an ergodic manner. Then, a new index of output transmission performance is proposed by investigating the mean value of the instantaneous power produced by the multiple actuation wrenches and one twist of the moving platform of one-DOF PMs. A local transmission index (LTI) is defined as the minimum value of the index of output and input transmission performance. A global transmission index (GTI) is then established based on the LTI. The proposed LTI and GTI are coordinate-free and have clear physical interpretation. Finally, the validity and universality of the new indices are demonstrated by optimization and analysis of redundantly actuated lower-mobility PMs with extra articulated six-DOF or limited-DOF limbs.

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.

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.

Singularity, isotropy, and velocity transmission evaluation of a three translational degrees-of-freedom parallel robot

Robotica ◽  
2012 ◽  
Vol 31 (2) ◽  
pp. 193-202 ◽  
Author(s):  
Yongjie Zhao
Keyword(s):  
Performance Evaluation ◽  
Angular Velocity ◽  
Degrees Of Freedom ◽  
Jacobian Matrix ◽  
Parallel Robot ◽  
End Effector ◽  
Transmission Index ◽  
Delta Robot ◽  
Singular Configuration ◽  
Velocity Transmission

SUMMARYPerformance evaluation of a parallel robot is a multicriteria problem. By taking Delta robot as an object of study, this paper presents the kinematic performance evaluation of a three translational degrees-of-freedom parallel robot from the viewpoint of singularity, isotropy, and velocity transmission. It is shown that the determinant of a Jacobian matrix cannot measure the distance from the singular configuration due to the existing inverse kinematic singularity of a Delta robot. The determinants of inverse and direct kinematic Jacobian matrices are adopted for the measurement of distance from the singular configuration based on the theory of numerical linear dependence. The denominator of the Jacobian matrix will be lost in the computation of the condition number when the end-effector is on the centerline of the workspace, so the Delta robot may also be nearly at a singular configuration when the condition number of the Jacobian matrix is equal to 1. The velocity transmission index whose physical meaning is the maximum input angular velocity when the end-effector translates in the unit velocity is presented. The evaluation of singularity, isotropy, and velocity transmission of a Delta robot is investigated by simulation. The velocity transmission index can also be used for the velocity transmission evaluation of a parallel robot with pure rotational degrees-of-freedom based on the principle of similarity. The physical meaning is modified to be the maximum input velocity when the end-effector rotates in the unit angular velocity.

A New Approach for Singularity Analysis and Closeness Measurement to Singularities of Parallel Manipulators

2012 ◽  
Vol 4 (4) ◽  
Author(s):  
Xin-Jun Liu ◽  
Chao Wu ◽  
Jinsong Wang
Keyword(s):  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Singularity Analysis ◽  
Challenging Problem ◽  
Performance Indices ◽  
New Approach ◽  
Singular Configurations ◽  
Different Types ◽  
Force Transmissibility ◽  
Singular Configuration

Singularity analysis is one of the most important issues in the field of parallel manipulators. An approach for singularity analysis should be able to not only identify all possible singularities but also explain their physical meanings. Since a parallel manipulator is always out of control at a singularity and its neighborhood, it should work far from singular configurations. However, how to measure the closeness between a pose and a singular configuration is still a challenging problem. This paper presents a new approach for singularity analysis of parallel manipulators by taking into account motion/force transmissibility. Several performance indices are introduced to measure the closeness to singularities. By using these indices, a uniform “metric” can be found to represent the closeness to singularities for different types of nonredundant parallel manipulators.

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.

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