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.

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.

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 a Class of Spherical Three-Degree-of Freedom Parallel Manipulators

1992 ◽  
Author(s):  
Clément M. Gosselin ◽  
Jaouad Sefrioui ◽  
Marc 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

Abstract 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.

Kinematics of a New High-Precision Three-Degree-of-Freedom Parallel Manipulator

2006 ◽  
Vol 129 (3) ◽  
pp. 320-325 ◽  
Author(s):  
Farhad Tahmasebi
Keyword(s):  
Power Dissipation ◽  
Inverse Kinematics ◽  
Parallel Manipulator ◽  
Degree Of Freedom ◽  
Base Plane ◽  
Degree Polynomial ◽  
Payload Capacity ◽  
Half Angle ◽  
Three Degree Of Freedom ◽  
Direct Kinematics

Closed-form direct and inverse kinematics of a new three-degree-of-freedom (DOF) parallel manipulator with inextensible limbs and base-mounted actuators are presented. The manipulator has higher resolution and precision than the existing three-DOF mechanisms with extensible limbs. Since all of the manipulator actuators are base mounted, higher payload capacity, smaller actuator sizes, and lower power dissipation can be obtained. The manipulator is suitable for alignment applications where only tip, tilt, and piston motions are significant. The direct kinematics of the manipulator is reduced to solving an eighth-degree polynomial in the square of the tangent of the half-angle between one of the limbs and the base plane. Hence, there are at most 16 assembly configurations for the manipulator. In addition, it is shown that the 16 solutions are eight pairs of reflected configurations with respect to the base plane. Numerical examples for the direct and inverse kinematics of the manipulator are also presented.

Determination of the Singularity Loci of Spherical Three-Degree-of-Freedom Parallel Manipularors

1992 ◽  
Author(s):  
Clément M. Gosselin ◽  
Jaouad Sefrioui
Keyword(s):  
Graphical Representation ◽  
Jacobian Matrix ◽  
Parallel Manipulators ◽  
Degree Of Freedom ◽  
End Effector ◽  
Cartesian Space ◽  
Singularity Locus ◽  
Three Degree Of Freedom ◽  
Analytical Expressions

Abstract In this paper, an algorithm for the determination of the singularity loci of spherical three-degree-of-freedom parallel manipulators with prismatic atuators is presented. These singularity loci, which are obtained as curves or surfaces in the Cartesian space, are of great interest in the context of kinematic design. Indeed, it has been shown elsewhere that parallel manipulators lead to a special type of singularity which is located inside the Cartesian workspace and for which the end-effector becomes uncontrollable. It is therfore important to be able to identify the configurations associated with theses singularities. The algorithm presented is based on analytical expressions of the determinant of a Jacobian matrix, a quantity that is known to vanish in the singular configurations. A general spherical three-degree-of-freedom parallel manipulator with prismatic actuators is first studied. Then, several particular designs are investigated. For each case, an analytical expression of the singularity locus is derived. A graphical representation in the Cartesian space is then obtained.

Kinematics of a New High Precision Three Degree-of-Freedom Parallel Manipulator

2005 ◽  
Author(s):  
Farhad Tahmasebi
Keyword(s):  
Power Dissipation ◽  
Inverse Kinematics ◽  
Parallel Manipulator ◽  
Degree Of Freedom ◽  
Base Plane ◽  
Degree Polynomial ◽  
Payload Capacity ◽  
Half Angle ◽  
Three Degree Of Freedom ◽  
Direct Kinematics

Closed-form direct and inverse kinematics of a new three degree-of-freedom (DOF) parallel manipulator with inextensible limbs and base-mounted actuators are presented. The manipulator has higher resolution and precision than the existing three DOF mechanisms with extensible limbs. Since all of the manipulator actuators are base-mounted; higher payload capacity, smaller actuator sizes, and lower power dissipation can be obtained. The manipulator is suitable for alignment applications where only tip, tilt, and piston motions are significant. The direct kinematics of the manipulator is reduced to solving an eighth-degree polynomial in the square of tangent of half-angle between one of the limbs and the base plane. Hence, there are at most sixteen assembly configurations for the manipulator. In addition, it is shown that the sixteen solutions are eight pairs of reflected configurations with respect to the base plane. Numerical examples for the direct and inverse kinematics of the manipulator are also presented.

Kinematic Isotropic Configuration of Spatial Cable-Driven Parallel Robots

2011 ◽  
Vol 1 (4) ◽  
pp. 61-86
Author(s):  
Hamoon Hadian ◽  
Abbas Fattah
Keyword(s):  
Parallel Manipulators ◽  
Parallel Robot ◽  
Numerical Approach ◽  
Parallel Robots ◽  
Degree Of Freedom ◽  
Tension Index ◽  
Symbolic Method ◽  
Three Degree Of Freedom ◽  
Cable Robots

In this paper, the authors study the kinematic isotropic configuration of spatial cable-driven parallel robots by means of four different methods, namely, (i) symbolic method, (ii) geometric workspace, (iii) numerical workspace and global tension index (GTI), and (iv) numerical approach. The authors apply the mentioned techniques to two types of spatial cable-driven parallel manipulators to obtain their isotropic postures. These are a 6-6 cable-suspended parallel robot and a novel restricted three-degree-of-freedom cable-driven parallel robot. Eventually, the results of isotropic conditions of both cable robots are compared to show their applications.

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