A tetrahedron approach for a unique closed-form solution of the forward kinematics of six-dof parallel mechanisms with multiconnected joints

2002 ◽  
Vol 19 (6) ◽  
pp. 269-281 ◽  
Author(s):  
Se-Kyong Song ◽  
Dong-Soo Kwon
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
Forward Kinematics ◽  
Parallel Mechanisms ◽  
Six Dof

Kinematics Analysis of a Novel 5-DOF Hybrid Manipulator

2015 ◽  
Vol 9 (6) ◽  
pp. 765-774 ◽  
Author(s):  
Wanjin Guo ◽  
◽  
Ruifeng Li ◽  
Chuqing Cao ◽  
Yunfeng Gao ◽  
...  
Keyword(s):  
Closed Form ◽  
Inverse Kinematics ◽  
Closed Form Solution ◽  
Form Solution ◽  
Parallel Mechanisms ◽  
Kinematics Analysis ◽  
Structure And Motion ◽  
Reachable Workspace ◽  
Hybrid Manipulator ◽  
Inverse Kinematics Problem

Application of hybrid robotics is a continuously developing field, as hybrid manipulators have demonstrated that they can combine the benefits of serial structures and parallel mechanisms. In this paper, a novel 5-degree-of-freedom hybrid manipulator is designed. The structure of this manipulator and its kinematics analysis are presented. An innovative closed-form solution was proposed to address the inverse kinematics problem. Additionally, the validity of the closed-form solution was verified via co-simulation using MATLAB and ADAMS. Finally, the reachable workspace of this manipulator was obtained for further optimizing the structure and motion control.

Analytical Study of Reachable Workspace for 2-RPR Planar Parallel Mechanisms

2012 ◽  
Author(s):  
Mahdi Agheli ◽  
Stephen S. Nestinger ◽  
Robert L. Norton
Keyword(s):  
Closed Form ◽  
Analytical Study ◽  
Structural Parameters ◽  
Closed Form Solution ◽  
High Accuracy ◽  
Form Solution ◽  
Parallel Mechanisms ◽  
Design And Optimization ◽  
Reachable Workspace ◽  
Selection Of

In both planar and spatial parallel mechanisms, selection of the structural parameters for a desired workspace generally employs the use of numerical methods. However, using the closed-form solution, if it exists, facilitates workspace-based design and optimization of the mechanism, and may significantly reduce the required time and calculation for finding the workspace of the mechanism. This paper presents a general and comprehensive closed-form solution for the reachable workspace of a 2-RPR planar parallel mechanism. The workspace of the mechanism is analyzed step-by-step in detail and its boundary is derived analytically. Since the solution is closed-form, it has high accuracy and reliability. Furthermore, the provided solution can be employed to solve the workspace of similar mechanisms in a closed-form manner including other n-RPR planar parallel mechanisms.

Forward Displacement Analysis of Parallel Mechanisms: Closed Form Solution of PRR-3S and PPR-3S Structures

1992 ◽  
Vol 114 (1) ◽  
pp. 68-73 ◽  
Author(s):  
V. Parenti-Castelli ◽  
C. Innocenti
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
Parallel Mechanisms ◽  
Algebraic Equations ◽  
Forward Displacement ◽  
Form Analysis ◽  
Displacement Analysis ◽  
Theoretical Results ◽  
Forward Displacement Analysis

The forward displacement analysis (FDA) in closed form of two classes of new parallel mechanisms derived from the Stewart Platform Mechanism (SPM) is presented in this paper. These mechanisms, when a set of actuator displacements is given, become multiloop structures of type PRR-3S and PPR-3S, with P, R and S for prismatic, revolute and spherical pairs, whereas the SPM has the structure RRR-3S. Solving the FDA in closed form means finding all the possible positions and orientations of the output controlled link when a set of actuator displacements is given, or equivalently, finding all possible closures of the corresponding structure. The closed form analysis of the PRR-3S and PPR-3S structures here presented results in algebraic equations in one unknown of degree 16 and 12, respectively. Hence 16 and 12 closures of the corresponding structures can be obtained. Numerical examples confirm these new theoretical results.

On a Closed-Form Solution of Prandtl's System of Equations

2013 ◽  
Vol 40 (2) ◽  
pp. 106-114
Author(s):  
J. Venetis ◽  
Aimilios (Preferred name Emilios) Sideridis
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
System Of Equations
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