Design and Analysis of a New Six-DOF Parallel Haptic Device With Singularity-Free Task Workspace

2008 ◽  
Author(s):  
Yi Yang ◽  
Yuru Zhang ◽  
Yaojun Zhang ◽  
Yonggang Cao
Keyword(s):  
Parallel Mechanism ◽  
Jacobian Matrix ◽  
Traditional Approach ◽  
Analytical Form ◽  
Singularity Analysis ◽  
Training System ◽  
Haptic Device ◽  
Physical Constraints ◽  
Singular Space ◽  
Six Dof

This paper presents a procedure to obtain a singularity-free task workspace with a new method to deal with singularities. In order to get an enlarged singularity-free task workspace, we first optimize the volume of the workspace, then we identify singularities in the optimal workspace, and finally we refine the singularity-free task workspace from the optimal workspace. The effects of four physical constraints on the workspace are analyzed, subject to which the optimization is realized. The traditional approach of singularity analysis is based on the Jacobian Matrix which is direct but has limitations, especially when the analytical form of the Jacobian is difficult to obtain. To solve this problem, we define a pseudo-singular space which encloses all singularity loci. By searching the pseudo-singular space numerically, we are able to obtain a singularity-free task workspace. We illustrate this method in the designing process of a 6-RSS parallel mechanism as a haptic device which has been integrated in a simulated dentist training system.

Kinematics of a 3-DOF Translational Parallel Mechanism With 3-PRPaR Topology

2004 ◽  
Author(s):  
Chung-Ching Lee ◽  
Jeng-Hong Chou
Keyword(s):  
Parallel Mechanism ◽  
Jacobian Matrix ◽  
Translational Motion ◽  
Analytical Form ◽  
Inverse Kinematic ◽  
Closed Form Solutions ◽  
The Matrix ◽  
Six Dof ◽  
Singular Configuration ◽  
Algebra Method

From the standpoint of kinematics, we present a type of three-dof pure spatial translational parallel mechanism with 3-PRPaR topology as an alternative to design automation devices and a regional structure of a six-dof hybrid parallel platform. First, we describe the structural properties of mechanism and analyze its kinematic mobility. It is verified that a pure translational motion does exist through the coordinate transformation technique and the well-known D-H parametric notations. Then, we proceed with the forward and inverse kinematic analysis and derive their analytical closed-form solutions by the matrix algebra method. For the confirmation of the derived equations, some numerical examples are also taken. Furthermore, with the help of the forward kinematics, we derive the workspace in the analytical form. Finally, taking account of the overall Jacobian matrix provides the condition number and the identification of singular configuration is explored based on direct and inverse kinematics Jacobian matrix.

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.

Kinematics and Singularity Analyses of a 2-RPU&SPR Parallel Manipulator

2013 ◽  
Vol 441 ◽  
pp. 568-571
Author(s):  
Jian Hui Fan ◽  
Bin Li ◽  
Xin Hua Zhao
Keyword(s):  
Numerical Simulations ◽  
Inverse Kinematics ◽  
Parallel Mechanism ◽  
Parallel Manipulator ◽  
Jacobian Matrix ◽  
Algebraic Method ◽  
Singularity Analysis

In this paper, kinematics and singularity of a 2-RPU&SPR parallel mechanism are analyzed by algebraic method. Firstly, the inverse kinematics of the parallel mechanism is derived. Secondly, the Jacobian matrix of the parallel mechanism is obtained and the singularity of the mechanism is analyzed. Finally, the correctness of singularity analysis of the mechanism is verified by numerical simulations.

Development of a novel two-limbed parallel mechanism having Schönflies motion

2014 ◽  
Vol 229 (1) ◽  
pp. 136-154 ◽  
Author(s):  
Sung Mok Kim ◽  
Kyoosik Shin ◽  
Byung-Ju Yi ◽  
Wheekuk Kim
Keyword(s):  
Parallel Mechanism ◽  
Kinematic Model ◽  
Singularity Analysis ◽  
Short Description ◽  
High Potential ◽  
Haptic Device ◽  
Line Geometry ◽  
Grassmann Line Geometry ◽  
Schönflies Motion ◽  
Very High

This paper introduces a novel parallel mechanism having Schönflies motion. The mechanism consists of only two RRPaR-type limbs. After a short description of its structure, its position analysis is conducted and its screw-based kinematic model is derived. Next, its singularity analysis is performed via Grassmann line geometry and then its optimal kinematic characteristics are examined with respect to workspace size and isotropy property. The results show that the proposed parallel mechanism has a very high potential to be used as a manipulator or a haptic device. A prototype of this mechanism was developed and tested to corroborate its performance.

One Novel Isoconstrained Parallel Robot With Schoenflies-Motion

2013 ◽  
Author(s):  
Po-Chih Lee
Keyword(s):  
Parallel Mechanism ◽  
Jacobian Matrix ◽  
Parallel Robot ◽  
Singularity Analysis ◽  
Point Of View ◽  
Universal Joint ◽  
Small Motion ◽  
Robot Architecture ◽  
Pick And Place ◽  
Pick And Place Operation

The coupling between two opposite bars of the hinged parallelogram produces relative 1-DoF circular translation and the opposite bars can move but remain parallel. From the point of view of kinematics, a hinged parallelogram is equivalent to a prismatic pair for a small motion. On the basis of a special parallel mechanism with the limb architecture of type CPUh (C and P denote cylindrical and prismatic pairs; Uh indicates the pseudo-universal-joint having one revolute and one screw pairs with the intersecting axes), we provide one novel Schoenflies-motion isoconstrained CPaUh//CPaUh robot with only two limbs having the hinged parallelograms for the fast pick-and-place operation of the assembly and packaging applications. This type of robot is compact for not only its structure but also its actuation. The robot architecture and kinematics including inverse and forward solutions are studied. In addition, Jacobian matrix, singularity analysis and workspace are further discussed. It is hoped that the evaluations of such two-limb parallel mechanism can be useful for possible application in industry where pick-and-place motion and higher accuracy are required.

Singularity Analysis of 6-PUS Vertical Parallel Mechanism

2013 ◽  
Vol 568 ◽  
pp. 129-134 ◽  
Author(s):  
Chao Qun Wang ◽  
Hong Tao Wu
Keyword(s):  
Dynamic Characteristics ◽  
Parallel Mechanism ◽  
Jacobian Matrix ◽  
Singularity Analysis ◽  
Stewart Platform ◽  
Analytic Singularity ◽  
Singularity Locus

Different from the general 6-SPS Stewart platform, 6-PUS parallel mechanism is a kind of fully parallel mechanism whose actuators are all fixed at the frame. The advantages of this mechanism are light movable mass, small inertia and good dynamic characteristics. This paper is focused on the singularity analysis of the 6-PUS parallel mechanism. Based on the Jacobian matrix which is derived from the kinematical equation, the analytic singularity locus equations are obtained and the three types singularities of the parallel mechanism are analyzed. Moreover, the position-singularity of the mechanism is discussed through some specific examples.

On the Design of Singularity-Free Cable-Driven Parallel Mechanism Based on Grassmann Geometry

2012 ◽  
Author(s):  
Yu Zou ◽  
Yuru Zhang ◽  
Yaojun Zhang
Keyword(s):  
Parallel Mechanism ◽  
Jacobian Matrix ◽  
Singularity Analysis ◽  
Geometric Meaning ◽  
Parallel Mechanisms ◽  
Line Geometry ◽  
Singular Configurations ◽  
Negative Effect ◽  
Grassmann Line Geometry ◽  
Grassmann Geometry

This paper deals with the design of singularity-free cable-driven parallel mechanism. Due to the negative effect on the performance, singularities should be avoided in the design. The singular configurations of mechanisms can be numerically determined by calculating the rank of its Jacobian matrix. However, this method is inefficient and non-intuitive. In this paper, we investigate the singularities of planar and spatial cable-driven parallel mechanisms using Grassmann line geometry. Considering cables as line vectors in projective space, the singularity conditions are identified with clear geometric meaning which results in useful method for singularity analysis of the cable-driven parallel mechanisms. The method is applied to 3-DOF planar and 6-DOF spatial cable-driven mechanisms to determine their singular configurations. The results show that the singularities of both mechanisms can be eliminated by changing the dimensions of the mechanisms or adding extra cables.

Singularity Analysis of a New 2-DOF Parallel Tilter

2012 ◽  
Vol 224 ◽  
pp. 504-509
Author(s):  
Hai Dong Wang ◽  
Jing Sun ◽  
Yu Quan Bi ◽  
Mao Sheng Yang
Keyword(s):  
Parallel Mechanism ◽  
Jacobian Matrix ◽  
Singularity Analysis ◽  
Degree Of Freedom ◽  
Coordinate Transformations ◽  
Analytic Equation ◽  
Singular Configuration ◽  
Two Degree Of Freedom

One type of spatial new parallel mechanism with two degree of freedom is proposed.. The position and velocity analytic equation are constructed based on the coordinate transformations. Finally, the singular configuration of the tilter is analyzed by the forward and the inverse Jacobian matrix.

Kinematic Analysis and Design of 3-RPSR Parallel Mechanism with Triple Revolute Joints on the Base

2010 ◽  
Vol 4 (4) ◽  
pp. 346-354 ◽  
Author(s):  
Yukio Takeda ◽  
◽  
Xiao Xiao ◽  
Kazuya Hirose ◽  
Yoshiki Yoshida ◽  
...  
Keyword(s):  
Kinematic Analysis ◽  
Parallel Mechanism ◽  
Jacobian Matrix ◽  
Large Angle ◽  
Vertical Axis ◽  
Output Link ◽  
Analysis And Design ◽  
Revolute Joints ◽  
Full Rotation ◽  
Six Dof

The present paper proposes a new six-DOF parallel mechanism with three connecting chains. This mechanism can have a large angle of orientation of the output link. Joints in each connecting chain are arranged from the base in order of revolute, prismatic, spherical and revolute joints. All three revolute joints on the base are coaxial. With this structure, the output link can perform a full rotation around the vertical axis. The orientation capability of this mechanism is demonstrated. Equations for displacement analysis and the Jacobian matrix are derived. A design and prototype of this mechanism for a pipe-bender are shown.

Variable Motion/Force Transmissibility of a Metamorphic Parallel Mechanism With Reconfigurable 3T and 3R Motion

2015 ◽  
Author(s):  
Dongming Gan ◽  
Jian S. Dai ◽  
Jorge Dias ◽  
Lakmal D. Seneviratne
Keyword(s):  
Parallel Mechanism ◽  
Jacobian Matrix ◽  
Screw Theory ◽  
Singularity Analysis ◽  
Design Parameters ◽  
Force Transmission ◽  
Pure Rotation ◽  
Rotation Axes ◽  
Potential Applications ◽  
Force Transmissibility

This paper presents a metamorphic parallel mechanism which can switch its motion between pure translation (3T) and pure rotation (3R) motion. This feature stems from a reconfigurable Hooke (rT) joint of which one of the rotation axes can be altered freely. More than that, based on the reconfiguration of the rT joint, workspace of both 3T and 3R motion can be tunable and the rotation center of the 3R motion can be controlled along a line perpendicular to the base plane. Kinematics analysis is presented based on the geometric constraint of the parallel mechanism covering both 3T and 3R motion. Following these screw theory based motion/force transmission equations are obtained and their characteristics are investigated and linked to the singularity analysis using Jacobian matrix. Motion/force transmission indices can be used to optimize basic design parameters of the metamorphic parallel mechanism. This provides reference of this mechanism for potential applications requiring 3T and 3R motion.

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