Fully-Isotropic Redundantly-Actuated Parallel Wrists With Three Degrees of Freedom

2007 ◽  
Author(s):  
Grigore Gogu
Keyword(s):  
Degrees Of Freedom ◽  
Jacobian Matrix ◽  
Velocity Space ◽  
Structural Synthesis ◽  
Linear Transformations ◽  
Force And Motion ◽  
Redundantly Actuated ◽  
Joint Velocity ◽  
First Time ◽  
Three Degrees Of Freedom

The paper presents fully-isotropic redundantly-actuated parallel wrists (RaPWs) with three degrees of freedom. The mobile platform has three independent rotations. A method is proposed for structural synthesis of fully-isotropic RaPWs based on the theory of linear transformations. A one-to-one correspondence exists between the actuated joint velocity space and the external velocity space of the moving platform. The Jacobian mapping the two vector spaces of fully-isotropic RaPWs presented in this paper is 3×3 identity matrix throughout the entire workspace. The condition number and the determinant of the Jacobian matrix being equal to one, the manipulator performs very well with regard to force and motion transmission capabilities. Redundant actuation is used to obtain fully-isotropic parallel wrists with three degrees of freedom. As far as we are aware, this paper presents for the first time in the literature the use of redundancy to design fully-isotropic parallel wrists as well as solutions of fullyisotropic RaPWs with three degrees of freedom.

Fully-Isotropic T1R2-Type Parallel Robots With Three Degrees of Freedom

2005 ◽  
Author(s):  
Grigore Gogu
Keyword(s):  
Degrees Of Freedom ◽  
Jacobian Matrix ◽  
Parallel Manipulators ◽  
Parallel Robots ◽  
Velocity Space ◽  
Linear Transformations ◽  
Matrix Mapping ◽  
Joint Velocity ◽  
First Time ◽  
Three Degrees Of Freedom

The paper presents singularity-free fully-isotropic T1R2-type parallel manipulators (PMs) with three degrees of freedom. The mobile platform has one independent translation (T1) and two rotations (R2). A method is proposed for structural synthesis of fully-isotropic T1R2-type PMs based on the theory of linear transformations. A one-to-one correspondence exists between the actuated joint velocity space and the external velocity space of the moving platform. The Jacobian matrix mapping the two vector spaces of fully-isotropic T1R2-type PMs presented in this paper is the 3x3 identity matrix throughout the entire workspace. The condition number and the determinant of the Jacobian matrix being equal to one, the manipulator performs very well with regard to force and motion transmission capabilities. As far as we are aware, this paper presents for the first time in the literature solutions of singularity-free T1R2-type PMs with decoupled an uncoupled motions, along with the fully-isotropic solutions.

Structural synthesis of maximally regular T3R2-type parallel robots via theory of linear transformations and evolutionary morphology

Robotica ◽  
2009 ◽  
Vol 27 (1) ◽  
pp. 79-101 ◽  
Author(s):  
G. Gogu
Keyword(s):  
Degrees Of Freedom ◽  
Jacobian Matrix ◽  
Parallel Robots ◽  
Velocity Space ◽  
Evolutionary Morphology ◽  
Structural Synthesis ◽  
Real Time Control ◽  
Linear Transformations ◽  
Time Control ◽  
Moving Platform

SUMMARYThe paper presents structural synthesis of maximally regular T3R2-type parallel robotic manipulators (PMs) with five degrees of freedom. The moving platform has three independent translations (T3) and two rotations (R2). A method is proposed for structural synthesis of maximally regular T3R2-type PMs based on the theory of linear transformations and evolutionary morphology. A one-to-one correspondence exists between the actuated joint velocity space and the external velocity space of the moving platform. The Jacobian matrix mapping the two vector spaces of maximally regular T3R2-type PMs presented in this paper is the 5×5 identity matrix throughout the entire workspace. The condition number and the determinant of the Jacobian matrix being equal to one, the manipulator performs very well with regard to force and motion transmission capabilities. Kinematic analysis of maximally regular parallel robots is trivial and no computation is required for real-time control. This paper presents in a unified approach the structural synthesis of PMs with five degrees of freedom with decoupled and uncoupled motions, along with the maximally regular solutions.

Architecture Optmization of a 3-DOF Parallel Mechanism

1998 ◽  
Author(s):  
J. A. Carretero ◽  
R. P. Podhorodeski ◽  
M. Nahon
Keyword(s):  
Parallel Mechanism ◽  
Architectural Design ◽  
Degrees Of Freedom ◽  
Jacobian Matrix ◽  
Design Parameters ◽  
Objective Functions ◽  
Constraint Equations ◽  
Three Degree Of Freedom ◽  
Architecture Optimization ◽  
Three Degrees Of Freedom

Abstract This paper presents a study of the architecture optimization of a three-degree-of-freedom parallel mechanism intended for use as a telescope mirror focussing device. The construction of the mechanism is first described. Since the mechanism has only three degrees of freedom, constraint equations describing the inter-relationship between the six Cartesian coordinates are given. These constraints allow us to define the parasitic motions and, if incorporated into the kinematics model, a constrained Jacobian matrix can be obtained. This Jacobian matrix is then used to define a dexterity measure. The parasitic motions and dexterity are then used as objective functions for the optimizations routines and from which the optimal architectural design parameters are obtained.

Dynamic Analysis of a Biglide Parallel Grinder

2005 ◽  
Vol 291-292 ◽  
pp. 495-500
Author(s):  
Ping Zou
Keyword(s):  
Machine Tool ◽  
Dynamic Analysis ◽  
Degrees Of Freedom ◽  
Jacobian Matrix ◽  
Lagrangian Formulation ◽  
Dynamic Equations ◽  
Six Degrees Of Freedom ◽  
Moving Platform ◽  
Drill Point ◽  
Joint Velocity

In this paper, the moving platform of the biglide parallel grinder with six degrees of freedom will keep moving horizontally at any time using parallelograms. Besides grinding the helical drill point, this grinder also can work as drilling and welding machine tool as well as a CMM. The joint-velocity Jacobian matrix is calculated. Moreover, the dynamic equations are derived by applying the Lagrangian formulation.

Parallel mechanisms with decoupled rotation of the moving platform in planar motion

2009 ◽  
Vol 224 (3) ◽  
pp. 709-720 ◽  
Author(s):  
G Gogu
Keyword(s):  
Translational Motion ◽  
Planar Motion ◽  
Parallel Mechanisms ◽  
Structural Synthesis ◽  
Linear Transformations ◽  
New Family ◽  
Current Article ◽  
Moving Platform ◽  
First Time

The current article presents a new family of T2R1-type spatial parallel mechanisms (PMs) with decoupled and unlimited rotation of the moving platform in planar motion. The moving platform performs two independent translations (T2) and one independent unlimited rotation (R1) whose axis is perpendicular to the plane of translations. A method is proposed for structural synthesis of T2R1-type PMs based on the theory of linear transformations. The moving platform has unlimited rotational capabilities and is decoupled with respect to translational motion. To the best of the author's knowledge, this article presents for the first time solutions of T2R1-type spatial PMs with decoupled and unlimited rotation of the moving platform in planar motion.

Design, kinematic and dynamic modeling of a novel tripod based manipulator

Robotica ◽  
2014 ◽  
Vol 34 (10) ◽  
pp. 2186-2204 ◽  
Author(s):  
Dan Zhang ◽  
Bin Wei
Keyword(s):  
Set Theory ◽  
Dynamic Modeling ◽  
Degrees Of Freedom ◽  
Jacobian Matrix ◽  
General Function ◽  
Multi Objective Optimization ◽  
Gf Set ◽  
Hybrid Manipulator ◽  
New Type ◽  
Three Degrees Of Freedom

SUMMARYThis paper proposes a novel three-degrees-of-freedom (3-DOF) hybrid manipulator, 3PU*S-PU, which evolves from the general function (Gf) set theory. After discussing the advantages of this new type of hybrid manipulator, this report analyzes the kinematic and Jacobian matrix of the manipulator. Subsequently, the kinematic performances, including stiffness/compliance, and workspace, undergo analysis, followed by the multi-objective optimization of the compliance and workspace. The Lagrangian method provides the framework for briefly analyzing the dynamics of the proposed manipulator. Finally, the results of this assessment comprise a guideline for controlling the manipulator.

Design and kinematic analysis of redundantly actuated parallel mechanisms for ankle rehabilitation

Robotica ◽  
2014 ◽  
Vol 33 (2) ◽  
pp. 366-384 ◽  
Author(s):  
Congzhe Wang ◽  
Yuefa Fang ◽  
Sheng Guo ◽  
Changchun Zhou
Keyword(s):  
Degrees Of Freedom ◽  
Control Strategies ◽  
Structural Characteristics ◽  
Parallel Mechanisms ◽  
Spherical Mechanisms ◽  
Ankle Rehabilitation ◽  
Redundantly Actuated ◽  
Reconfigurable Capacity ◽  
Three Degrees Of Freedom ◽  
Rehabilitation Exercise

SUMMARYIn this paper, we present the design of two serial spherical mechanisms to substitute for a single spherical joint that is usually used to connect the platform with the base in three degrees of freedom parallel mechanisms. According to the principle derived from the conceptual design, through using the two serial spherical mechanisms as the constraint limb, several redundantly actuated parallel mechanisms are proposed for ankle rehabilitation. The proposed parallel mechanisms all can perform the rotational movements of the ankle in three directions while at the same time the mechanism center of rotations can match the ankle axes of rotations compared with other multi-degree-of-freedom devices, due to the structural characteristics of the special constraint limb and platform. Two special parallel mechanisms are selected to analyze their kinematical performances, such as workspace, dexterity, singularity, and stiffness, based on the computed Jacobian. The results show that the proposed scheme of actuator redundancy can guarantee that the redundantly actuated parallel mechanisms have no singularity, better dexterity, and stiffness within the prescribed workspace in comparison with the corresponding non-redundant parallel mechanisms. In addition, the proposed mechanisms possess certain reconfigurable capacity based on control strategies or rehabilitation modes to obtain sound performance for completing ankle rehabilitation exercise.

Reliability and Efficiency of the Existing Spectral Methods for Isomorphism Detection

2005 ◽  
Vol 128 (6) ◽  
pp. 1246-1252 ◽  
Author(s):  
Rajesh Pavan Sunkari ◽  
Linda C. Schmidt
Keyword(s):  
Characteristic Polynomial ◽  
Degrees Of Freedom ◽  
Polynomial Method ◽  
Worst Case ◽  
Frobenius Theorem ◽  
Spectral Techniques ◽  
Kinematic Chains ◽  
Correct Proof ◽  
First Time ◽  
Three Degrees Of Freedom

Mechanism researchers have developed several types of codes and indices, to indicate if a pair of kinematic chains is isomorphic. Unfortunately, most of these codes or indices are either computationally inefficient or unreliable. This work establishes, for the first time, the reliability of the existing spectral techniques—characteristic polynomial and eigenvector approaches—for isomorphism detection. The reliability of characteristic polynomial of adjacency matrix is established by determining the number of pairs of non-isomorphic chains, with up to 14 links and one, two, and three degrees of freedom. The most recent eigenvector approach is critically reviewed and correct proof is provided for the statement that is the basis for this approach. It is shown, for the first time, that the eigenvector approach was able to identify all nonisomorphic chains, with up to 14 links and one, two, and three degrees of freedom. It is shown that unlike the characteristic polynomial method the eigenvector approach in worst case might take exponential time. Finally, efficient methods are suggested to the classical eigenvector approach by using the Perron–Frobenius theorem.

Structural synthesis of a class of 3-DOF wrist mechanisms with redundantly-actuated closed-loop units

2015 ◽  
Vol 230 (2) ◽  
pp. 276-290 ◽  
Author(s):  
Haibo Qu ◽  
Yuefa Fang ◽  
Sheng Guo
Keyword(s):  
Degrees Of Freedom ◽  
Closed Loop ◽  
Screw Theory ◽  
Open Loop ◽  
Structural Synthesis ◽  
Constraint System ◽  
Redundantly Actuated ◽  
Rotational Degrees Of Freedom ◽  
Moving Platform

In this paper, a new method is proposed for the structural synthesis of a class of redundantly-actuated parallel wrists (RaPWs) with three rotational degrees of freedom of the moving platform and symmetrical structures based on screw theory. First, the new procedure for structural synthesis of RaPWs with closed-loop actuated unit is proposed and the constraint system of the moving platform of RaPWs is analyzed. Then, considering the inclusion relation between the primary constraint system and the limb constraint system, the type of kinematic limb is determined. The synthesis of type-1 and type-2 kinematic limbs is dealt with based on the obtained closed-loop actuated unit and open-loop sub-limb. Next, the RaPWs are synthesized and a number of new RaPWs have been identified. Finally, the condition for proper actuator selections of RaPWs is revealed, and one example is used to perform the validation.

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