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.

Kinematics of a H-Type Pure Translational Parallel Manipulator

2005 ◽  
Author(s):  
Chung-Ching Lee ◽  
Jeng-Hong Chiu ◽  
Hung-Hui Wu
Keyword(s):  
Parallel Manipulator ◽  
Jacobian Matrix ◽  
Translational Motion ◽  
Inverse Kinematic ◽  
Closed Form Solutions ◽  
Algebra Approach ◽  
The Matrix ◽  
Six Dof ◽  
Inverse Kinematic Analysis ◽  
Parallel Platform

From the viewpoint of kinematics, a three-dof H-type pure translational parallel manipulator is presented for the development of automatic assembly devices and a regional structure of a six-dof hybrid parallel platform. First, we describe the structural properties of manipulator and analyze its kinematic mobility. A pure translational motion is verified to exist through the well-known D-H symbolic notations and the coordinate transformation technique. What follows are the forward and inverse kinematic analysis and their analytical closed-form solutions by the matrix algebra approach. For further confirmation of the derived equations, some numerical examples are also given. Moreover, with the help of the analytical displacement kinematics, we identify the volume of workspace. At last, taking account of the overall Jacobian matrix provides the condition number and the identification of singularity of configuration is explored based on the direct and inverse kinematics Jacobian matrix.

Kinematics of a Prism-Type Translational Robot

2009 ◽  
Author(s):  
Chung-Ching Lee ◽  
Po-Chih Lee
Keyword(s):  
Inverse Kinematics ◽  
Jacobian Matrix ◽  
Translational Motion ◽  
Parallel Robot ◽  
Kinematics Analysis ◽  
Closed Form Solutions ◽  
Algebra Approach ◽  
The Matrix ◽  
Six Dof ◽  
Parallel Platform

From the viewpoint of kinematics, a three-dof Prism-type pure translational parallel robot is presented for the development of automatic assembly devices and a regional structure of a six-dof hybrid parallel platform. First, we describe the structural properties of the robot and analyze its kinematic mobility. A pure translational motion is verified to exist through the well-known D-H symbolic notations and the coordinate-transformation-matrix technique. What follows are the forward, inverse kinematics analysis, and their closed-form solutions by the matrix algebra approach. For further confirmation of the correctness of derived equations, some numerical examples are also given. With the help of the analytical displacement kinematics, we identify the volume of workspace. At last, taking account of the 3×3 reduced Jacobian matrix provides the condition number and the identification of singularity of configuration is explored based on the direct and inverse kinematics Jacobian matrix.

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.

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.

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 of a Novel Translational Platform

2003 ◽  
Vol 125 (2) ◽  
pp. 308-315 ◽  
Author(s):  
Massimo Callegari ◽  
Matteo Tarantini
Keyword(s):  
Closed Form ◽  
Kinematic Analysis ◽  
Parallel Mechanism ◽  
Simple Structure ◽  
Jacobian Matrix ◽  
Differential Analysis ◽  
Symbolic Expression ◽  
Closed Form Solutions ◽  
Design Considerations ◽  
Working Space

A new three-d.o.f. parallel mechanism, with 3-RPC topology, is presented in the paper and its kinematics is studied. The proposed architecture, if proper geometrical conditions are satisfied, has an overconstrained structure which allows motions of pure translation. The simple structure of the mechanism allows finding closed-form solutions for both inverse and direct position kinematics; the differential analysis has been developed as well, by deriving a symbolic expression for the Jacobian matrix. Then, some design considerations are exposed to keep the singular points out of the working space of the mechanism and all the isotropic configurations are eventually identified.

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.

Four Novel Pick-and-Place Isoconstrained Manipulators and Their Inverse Kinematics

2010 ◽  
Author(s):  
Po-Chih Lee ◽  
Jyh-Jone Lee ◽  
Chung-Ching Lee
Keyword(s):  
Inverse Kinematics ◽  
Inverse Kinematic ◽  
Parallel Mechanisms ◽  
Universal Joint ◽  
Industrial Assembly ◽  
Pick And Place ◽  
The Matrix ◽  
Potential Applications ◽  
Algebra Method ◽  
Pick And Place Operation

The four-degree-of-freedom (4-DoF) Schoenflies-motion (briefly termed X-motion) manipulator with the fast pick-and-place operation is essential for industrial assembly and packaging. For the development of this kind of industrial manipulator, we provide architectures and inverse kinematics of four X-motion isoconstrained parallel mechanisms with two limbs, CuuUwHw-//-CvvUwHw, CuRuuUhw-//-CvRvvUhw, CuRuPHw-//-CvRvPHw and CuPuUhw-//-CvPvUhw (R, P, H and C denote revolute, prismatic, screw and cylindrical pairs respectively; U indicates a universal joint). These novel manipulators are excerpted from numerous general architectural types of isoconstrained parallel generators of X-motion. In this work, their architectures and mobility are first elucidated in detail. With the help of the well-known D-H symbolic notations, their three translational and one rotational motion are comprehensively verified through the four-by-four coordinate transformation matrix approach. Inverse kinematic solutions of joint displacements of each manipulator are further established by using the matrix algebra method for the reference of potential applications.

Study on Delta Parallel Mechanism Kinematics and Singularity Based on Inverse Solution

2010 ◽  
Vol 43 ◽  
pp. 114-118
Author(s):  
Zhong Jie Chen ◽  
Qui Ju Zhang ◽  
Chun Jian Hua
Keyword(s):  
Optimal Design ◽  
Kinematic Analysis ◽  
Parallel Mechanism ◽  
Jacobian Matrix ◽  
Acceptable Range ◽  
Inverse Solutions ◽  
Singular Configuration ◽  
And Control ◽  
The Impact ◽  
The Relationship

In this paper, the kinematic analysis on a 3-DOF Delta parallel mechanism was carried out and the relationship models between the end cell output motions and the master arms input parameters were established. The forward and inverse solutions to position, velocity and acceleration were deduced and then verified by simulation, the curves that gotten by calculation and simulation were smooth, and no mutations or jumps appeared. In the meantime, based on the kinematic analysis, the impact of Jacobian matrix on the manipulator singular configuration was discussed, and the maneuverability in the reachable space was obtain quantitatively, meanwhile, the value of cond(C(Jv)) was located in the acceptable range, which approached to the isotropic value, so, the theory basis for optimal design was provided. The methods and conclusions in this paper are helpful to the design and control of 3-DOF Delta parallel mechanism.

scholarly journals A New Approach of Soft Joint Based on a Cable-Driven Parallel Mechanism for Robotic Applications

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1468
Author(s):  
Luis Nagua ◽  
Carlos Relaño ◽  
Concepción A. Monje ◽  
Carlos Balaguer
Keyword(s):  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Kinematic Model ◽  
Experimental Tests ◽  
Humanoid Robots ◽  
Inverse Kinematic ◽  
Element Analysis ◽  
New Approach ◽  
Flexible Polymer ◽  
The Mathematical Model

A soft joint has been designed and modeled to perform as a robotic joint with 2 Degrees of Freedom (DOF) (inclination and orientation). The joint actuation is based on a Cable-Driven Parallel Mechanism (CDPM). To study its performance in more detail, a test platform has been developed using components that can be manufactured in a 3D printer using a flexible polymer. The mathematical model of the kinematics of the soft joint is developed, which includes a blocking mechanism and the morphology workspace. The model is validated using Finite Element Analysis (FEA) (CAD software). Experimental tests are performed to validate the inverse kinematic model and to show the potential use of the prototype in robotic platforms such as manipulators and humanoid robots.

Sign in / Sign up

Export Citation Format

Share Document