Reciprocal screw theory based singularity analysis of a novel 3-DOF parallel manipulator

This work is devoted to simplify the inverse–forward kinematics of a parallel manipulator generator of the 3T1R motion. The closure equations of the displacement analysis are formulated based on the coordinates of two points embedded in the moving platform. Afterward, five quadratic equations are solved by means of a novel method based on Gröbner bases endowed with first-order perturbation and local stability of parameters. Meanwhile, the input–output equations of velocity and acceleration are systematically obtained by resorting to reciprocal-screw theory. In that concern, the inclusion of pseudokinematic pairs connecting the limbs to the fixed platform and a passive kinematic chain to the robot manipulator allows to avoid the handling of rank-deficient Jacobian matrices. The workspace of the robot is determined by using a discretized method associated to its inverse–forward displacement analysis, whereas the singularity analysis is approached based on the input–output equation of velocity. Numerical examples are provided with the purpose to show the application of the method.

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Geometrical method to determine the reciprocal screws and applications to parallel manipulators

Robotica ◽

10.1017/s0263574709005359 ◽

2009 ◽

Vol 27 (6) ◽

pp. 929-940 ◽

Cited By ~ 26

Author(s):

Jianguo Zhao ◽

Bing Li ◽

Xiaojun Yang ◽

Hongjian Yu

Keyword(s):

Parallel Manipulator ◽

Screw Theory ◽

Parallel Manipulators ◽

Singularity Analysis ◽

Algebraic Manipulation ◽

Robot Kinematics ◽

Geometrical Approach ◽

New Approach ◽

Geometrical Relation ◽

Manipulator Design

SUMMARYScrew theory has demonstrated its wide applications in robot kinematics and statics. We aim to propose an intuitive geometrical approach to obtain the reciprocal screws for a given screw system. Compared with the traditional Plücker coordinate method, the new approach is free from algebraic manipulation and can be used to obtain the reciprocal screws just by inspecting the structure of manipulator. The approach is based on three observations that describe the geometrical relation for zero pitch screw and infinite pitch screw. Based on the observations, the reciprocal screw systems of several common kinematic elements are analyzed, including usual kinematic pairs and chains. We also demonstrate usefulness of the geometrical approach by a variety of applications in mobility analysis, Jacobian formulation, and singularity analysis for parallel manipulator. This new approach can facilitate the parallel manipulator design process and provide sufficient insights for existing manipulators.

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Optimal Design and Singularity Analysis of a Spatial Parallel Manipulator

Symmetry ◽

10.3390/sym11040551 ◽

2019 ◽

Vol 11 (4) ◽

pp. 551 ◽

Cited By ~ 1

Author(s):

Xiaoyong Wu

Keyword(s):

Optimal Design ◽

Mechanism Design ◽

Parallel Manipulator ◽

Screw Theory ◽

Kinematic Model ◽

Singularity Analysis ◽

Singular Configurations ◽

Simulation Results ◽

Optimal Configurations

Optimal design and singularity analysis are two important aspects of mechanism design, and they are discussed within a spatial parallel manipulator in this work. Resorting to matrix transformation, the parametric kinematic model is established, upon which the inverse position and Jacobian are analyzed. As for optimal design, dexterity and payload indices are taken into consideration. From the simulation results, two optimal configurations are obtained, namely, the star-shaped one and the T-shaped one, and they respectively own the best payload performance and the best dexterity performance. Moreover, the concept of shape singularity is introduced and generalized, which is a special type of singularity that will lead to the singularity in all configurations. The shape singularity of the proposed manipulator is indicated by dexterity index and identified by screw theory. A case study is presented to demonstrate the implication of the shape singularity. Both optimal and singular configurations are useful, and new devices can thus be envisaged for this type of application.

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Kinematic and Singularity Analysis of a Novel 4-DOF Parallel Manipulator

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.101-102.685 ◽

2011 ◽

Vol 101-102 ◽

pp. 685-688 ◽

Cited By ~ 1

Author(s):

Meng Guan ◽

Yi Min Song ◽

Tao Sun ◽

Gang Dong

Keyword(s):

Kinematic Analysis ◽

Parallel Manipulator ◽

Jacobian Matrix ◽

Screw Theory ◽

Singularity Analysis ◽

Inverse Kinematic ◽

Degree Of Freedom ◽

Velocity Analysis ◽

Inverse Kinematic Analysis ◽

In Virtue Of

This paper presents a novel 4-DOF (Degree of Freedom) parallel manipulator called 2-PSS&(2-PRR)R manipulator. Firstly, the architecture of this manipulator is described and the mobility is analyzed via screw theory. Secondly, the inverse kinematic analysis including position analysis and velocity analysis is performed. Finally, the Jacobian matrix is obtained through velocity analysis, and then three kinds of singularity configurations are observed in virtue of the Jacobian matrix. This paper lays the foundation for further research of this manipulator.

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The Singularity Analysis of 3-RPS Parallel Manipulator

Volume 2: 30th Annual Mechanisms and Robotics Conference, Parts A and B ◽

10.1115/detc2006-99028 ◽

2006 ◽

Cited By ~ 2

Author(s):

Yanwen Li ◽

Zhen Huang ◽

Lumin Wang

Keyword(s):

Parallel Manipulator ◽

Screw Theory ◽

Dimensional Space ◽

Three Dimensional ◽

Singularity Analysis ◽

Necessary Condition ◽

Line Geometry ◽

Simple Singularity ◽

Sufficient And Necessary Condition ◽

Three Dimensional Space

This paper firstly introduces a kinematic principle of singularity. It is a sufficient and necessary condition to identify singularity. Using the condition this paper systematically studies the singularity of 3-RPS parallel manipulator. A simple singularity equation is derived and the complete singularity loci in the three-dimensional space are illustrated. In order to analyze the singularity property and verify the correctness of the derived equation the line-geometry and the constraint screw theory are used. Some important singularity properties and the distribution characteristics are presented.

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Performance evaluation of a special 6-PUS type parallel manipulator

Robotica ◽

10.1017/s0263574721000655 ◽

2021 ◽

pp. 1-15

Author(s):

Xiaochu Liu ◽

Yunfei Cai ◽

Weitian Liu ◽

Linlong Zhang ◽

Chengxin Hu

Keyword(s):

Performance Evaluation ◽

Natural Frequency ◽

Parallel Manipulator ◽

Screw Theory ◽

Shaking Table ◽

Axial Stiffness ◽

Neutral Position ◽

Dynamics Model ◽

Force Transmissibility ◽

Kane Method

Abstract In this paper, a special 6-PUS parallel manipulator (PM) is utilized as a shaking table. Unlike the existing results about 6-PUS PMs, we make the actuator direction collinear with the linkage direction at neutral position. With respect to the application background, a further analysis of the special PM is carried out from the perspective of motion/force transmissibility, natural frequency and acceleration capability. Specially, the complete dynamics model is established based on the Kane method. Then, generalized transmission indices based on the screw theory are utilized to reflect its motion ability, and a model of natural frequency is proposed with the axial stiffness of linkages considered. Finally, the effect of the angle between the actuator direction and the linkage direction α on various performances is analyzed, and other results are included to illustrate its feasibility and usability.

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Structure Synthesis of 3-RRS Type Spatial Compliant Parallel Manipulator

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.44-47.1375 ◽

2010 ◽

Vol 44-47 ◽

pp. 1375-1379

Author(s):

Da Chang Zhu ◽

Li Meng ◽

Tao Jiang

Keyword(s):

Parallel Manipulator ◽

Compliant Mechanisms ◽

Screw Theory ◽

Weight Ratio ◽

Parallel Manipulators ◽

Robot System ◽

New Approach ◽

Structure Synthesis ◽

Rigid Joints ◽

Type 3

Parallel manipulators has been extensively studied by virtues or its high force-to-weight ratio and widely spread applications such as vehicle or flight simulator, a machine tool and the end effector of robot system. However, as each limb includes several rigid joints, assembling error is demanded strictly, especially in precision measurement and micro-electronics. On the other hand, compliant mechanisms take advantage of recoverable deformation to transfer or transform motion, force, or energy and the benefits of compliant mechanisms mainly come from the elimination of traditional rigid joints, but the traditional displacement method reduce the stiffness of spatial compliant parallel manipulators. In this paper, a new approach of structure synthesis of 3-DoF rotational compliant parallel manipulators is proposed. Based on screw theory, the structures of RRS type 3-DoF rotational spatial compliant parallel manipulator are developed. Experiments via ANSYS are conducted to give some validation of the theoretical analysis.

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