A Closed-Form Solution for the Direct Kinematics of a Special Class of Spherical Three-Degree-of-Freedom Parallel Manipulators

1995 ◽  
pp. 231-240 ◽  
Author(s):  
C. M. Gosselin ◽  
M. Gagné
Keyword(s):  
Closed Form ◽  
Special Class ◽  
Closed Form Solution ◽  
Parallel Manipulators ◽  
Form Solution ◽  
Degree Of Freedom ◽  
Three Degree Of Freedom ◽  
Direct Kinematics

On the Direct Kinematics of Spherical Three-Degree-of-Freedom Parallel Manipulators of General Architecture

1994 ◽  
Vol 116 (2) ◽  
pp. 594-598 ◽  
Author(s):  
C. M. Gosselin ◽  
J. Sefrioui ◽  
M. J. Richard
Keyword(s):  
Parallel Manipulators ◽  
Degree Of Freedom ◽  
Real Solutions ◽  
Three Degree Of Freedom ◽  
General Architecture ◽  
Direct Kinematics

In this paper, the direct kinematics of general spherical parallel three-degree-of-freedom manipulators is investigated. A polynomial of degree 8 is obtained to describe this problem and it is shown that this polynomial is minimal since 8 real solutions corresponding to actual configurations have been found for a given set of actuator coordinates and a given architecture. This result completes the study on the direct kinematics of spherical three-degree-of-freedom parallel manipulators undertaken by the authors in a previous paper. An example of an architecture and a set of actuator coordinates which lead to 8 real solutions is presented to illustrate the results.

Closed form solution to the position workspace of Stewart parallel manipulators

1998 ◽  
Vol 41 (4) ◽  
pp. 393-403 ◽  
Author(s):  
Tian Huang ◽  
Jinsong Wang ◽  
D. J. Whitehouse
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Parallel Manipulators ◽  
Form Solution

On the Direct Kinematics of Spherical Three-Degree-of-Freedom Parallel Manipulators with a Coplanar Platform

1994 ◽  
Vol 116 (2) ◽  
pp. 587-593 ◽  
Author(s):  
C. M. Gosselin ◽  
J. Sefrioui ◽  
M. J. Richard
Keyword(s):  
Parallel Manipulator ◽  
Minimal Polynomial ◽  
Polynomial Solution ◽  
Parallel Manipulators ◽  
Degree Of Freedom ◽  
Real Solutions ◽  
Revolute Joints ◽  
Three Degree Of Freedom ◽  
Spherical Parallel Manipulator ◽  
Direct Kinematics

This paper presents a polynomial solution to the direct kinematic problem of a class of spherical three-degree-of-freedom parallel manipulators. This class is defined as the set of manipulators for which the axes of the three revolute joints attached to the gripper link are coplanar and symmetrically arranged. It is shown that, for these manipulators, the direct kinematic problem admits a maximum of 8 real solutions. A polynomial of degree 8 is obtained here to support this result and cases for which all the roots of the polynomial lead to real configurations are presented. Finally, the spherical parallel manipulator with collinear actuators, which received some attention in the literature, is also treated and is shown to lead to a minimal polynomial of the same degree. Examples of the application of the method to manipulators of each category are given and solved.

On the Direct Kinematics of General Spherical Three-Degree-of-Freedom Parallel Manipulators

1992 ◽  
Author(s):  
Clément M. Gosselin ◽  
Jaouad Sefrioui ◽  
Marc J. Richard
Keyword(s):  
Parallel Manipulators ◽  
Degree Of Freedom ◽  
Real Solutions ◽  
Three Degree Of Freedom ◽  
Direct Kinematics

Abstract In this paper, the direct kinematics of general spherical parallel three-degree-of-freedom manipulators is investigated. A polynomial of degree 8 is obtained to describe this problem and it is shown that this polynomial is minimal since 8 real solutions corresponding to actual configurations have been found for a given set of actuator coordinates and a given architecture. This result completes the study on the direct kinematics of spherical three-degre-of-freedom parallel manipulators undertaken by the authors in a previous paper. An example of an architecture and a set of actuator coordinates which lead to 8 real solutions is presented to illustrate the results.

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