Cartesian Parallel Manipulators With Pseudoplanar Limbs

2006 ◽  
Vol 129 (12) ◽  
pp. 1256-1264 ◽  
Author(s):  
Chung-Ching Lee ◽  
Jacques M. Hervé
Keyword(s):  
Lie Group ◽  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Degree Of Freedom ◽  
Linear Dependency ◽  
Algebraic Properties ◽  
Moving Platform ◽  
Three Degree Of Freedom

Based on the Lie-group-algebraic properties of the displacement set, the three-degree-of-freedom (3DOF) pseudoplanar motion often termed Y motion for brevity is first introduced. Then, all possible general architectures of the mechanical generators of a given Y subgroup are obtained by implementing serial arrays of 1DOF Reuleaux pairs or hinged parallelograms. In total, five distinct mechanical generators of Y motion are revealed and seven ones having at least one parallelogram are also derived from them. In order to avoid the singularity that may occur in the limbs, all singular postures of Y-motion generators are also located by detecting the possible linear dependency of the joint twists and the group dependency of displacement sets. The parallel layout of three 4DOF limbs including Y-motion generators with orthogonal planes make up a Cartesian translational parallel manipulator, which produces a motion set of spatial translations. The 3DOF translation of the moving platform is directly controlled by the three 1DOF translations in three orthogonal prismatic fixed joints.

Stiffness Analysis of Inverted Tripod Parallel Manipulator

2017 ◽  
Vol 867 ◽  
pp. 205-211
Author(s):  
T. Geethapriyan ◽  
R. Manoj Samson ◽  
T. Muthuramalingam ◽  
A.C. Arun Raj
Keyword(s):  
Parallel Manipulator ◽  
Degree Of Freedom ◽  
Ball Screw ◽  
Stiffness Analysis ◽  
Adams Software ◽  
Movable Platform ◽  
Moving Platform ◽  
Rotation Motion ◽  
Three Degree Of Freedom ◽  
Stewart Gough Platform

The concept of parallel manipulator is becoming more popular in modern manufacturing processes due to its various inherent advantages like rigidity, less inertia and accuracy. This project focuses on modeling, simulation and dynamic analysis of inverted tripod parallel manipulator which has three degree of freedom (1 transverse in z axis and rotation motion in x and y axis). The Stewart Gough parallel manipulator consists of moving platform connected to fixed platform with six links (6 Degree of Freedom).This inverted tripod parallel manipulator consists of movable platform connected to the fixed platform with only three links so it has better rigidity compared to Stewart Gough platform. The Stewart Gough parallel manipulator is considered to be highly stable because moving platform size is smaller than the fixed platform. Inverted type parallel manipulator consists of moving platform bigger than the fixed platform. So to improve the stiffness and precision ball screw is used for the support of links. The design of parallel manipulator is done considering rigidity, strength and efficiency of the system. The modeling of the tripod manipulator is done using PRO-E software. Kinematic analysis has been carried out and the stiffness analysis will be done by using ANSYS and ADAMS software.

Position Analysis, Workspace, and Optimization of a 3-P̱PS Spatial Manipulator

2009 ◽  
Vol 131 (5) ◽  
Author(s):  
M. Ruggiu
Keyword(s):  
Nonlinear System ◽  
Analytical Solution ◽  
Reference Point ◽  
Inverse Analysis ◽  
Parallel Manipulator ◽  
Direct Analysis ◽  
Degree Of Freedom ◽  
Position Analysis ◽  
Moving Platform ◽  
Three Degree Of Freedom

The present paper describes the analytical solution of position kinematics for a three degree-of-freedom parallel manipulator. It also provides a numeric example of workspace calculation and a procedure for its optimization. The manipulator consists of a base and a moving platform connected to the base by three identical legs; each leg is provided with a P̱PS chain, where P̱ designates an actuated prismatic pair, P stands for a passive prismatic pair, and S a spherical pair. The direct analysis yields a nonlinear system with eight solutions at the most. The inverse analysis is solved in three relevant cases: (i) the orientation of the moving platform is given, (ii) the position of a reference point of the moving platform is given, and (iii) two rotations (pointing) and one translation (focusing) are given. In the present paper it is proved that case (i) yields an inverse singularity condition of the mechanism; case (ii) provides a nonlinear system with four distinct solutions at the most; case (iii) allows the finding of some geometrical configurations of the actuated pairs for minimizing parasitic movements in the case of a pointing/focusing operation of the manipulator.

A novel relative degree-of-freedom criterion for a class of parallel manipulators with kinematic redundancy and its applications

2016 ◽  
Vol 231 (22) ◽  
pp. 4227-4240 ◽  
Author(s):  
Haibo Qu ◽  
Sheng Guo ◽  
Ying Zhang
Keyword(s):  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Open Loop ◽  
Degree Of Freedom ◽  
Relative Degree ◽  
Kinematic Redundancy ◽  
Mechanism Synthesis ◽  
Key Points ◽  
Moving Platform ◽  
The Difference

The mobility of a whole parallel manipulator and the relative degree-of-freedom are the key points in mechanism synthesis and analysis, which often can be used to verify the existence of mechanisms. In this paper, the difference between the mobility of a parallel manipulator and the relative degree-of-freedom is discussed. First, a novel relative degree-of-freedom criterion is proposed based on the principle of determining the moving platform by N point positions, which is suitable for a kind of parallel manipulator with spherical joints attached to the moving platform. Next, the relative degree-of-freedom criterion is used to calculate the independent motions of the moving platform compared with the modified Kutzbach–Grübler criterion. The proposed relative degree-of-freedom criterion is different from the modified Kutzbach–Grübler criterion in result value and physical meaning. Finally, the type synthesis of such parallel manipulator with open-loop limbs or closed-loop limbs is performed based on the proposed relative degree-of-freedom criterion.

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.

scholarly journals Spatial Three Degree of Freedom Parallel Manipulator Forward Kinematic Position Analysis

2018 ◽  
Vol 7 (4.5) ◽  
pp. 147
Author(s):  
Srinivasa Rao Pundru ◽  
Mohan Rao Nallur
Keyword(s):  
Parallel Manipulator ◽  
Linear Equations ◽  
Degree Of Freedom ◽  
Algebraic Equations ◽  
Position Analysis ◽  
Non Linear ◽  
Kinematic Position ◽  
Moving Platform ◽  
Forward Kinematic ◽  
Three Degree Of Freedom

This work presents forward kinematic position analysis of a spatial three degree of freedom parallel manipulator, which has three symmetric loops. The three loops consist of an actuated sliding links- rotational and spherical joints. The actuated sliding links are attached to inclined base platform via rotational joints. The limbs are connected from rotational joints to moving platform by spherical joints. The degree of freedom of a spatial parallel manipulator is analyzed via kutzbach criterion. The forward kinematic position analysis carried out by using 3-coupled trigonometric equations which are formulated with side and behaviour constraints of the manipulator. There are many difficulties in solving the system of non-linear equations in kinematics of manipulator therefore by using MATLAB the three non-linear coupled algebraic equations are solved. The forward position kinematic analysis part is used in the development procedure of spatial parallel manipulator to check, the required and obtained positions of the moving platform of the developed manipulator.  

Parallel Computational Algorithms for the Kinematics and Dynamics of Planar and Spatial Parallel Manipulators

1996 ◽  
Vol 118 (1) ◽  
pp. 22-28 ◽  
Author(s):  
C. M. Gosselin
Keyword(s):  
Inverse Kinematics ◽  
Parallel Manipulator ◽  
Inverse Dynamics ◽  
Parallel Manipulators ◽  
Degree Of Freedom ◽  
Kinematic Chains ◽  
Novel Approach ◽  
Judicious Choice ◽  
Six Degree Of Freedom ◽  
Three Degree Of Freedom

This paper introduces a novel approach for the computation of the inverse dynamics of parallel manipulators. It is shown that, for this type of manipulator, the inverse kinematics and the inverse dynamics procedures can be easily parallelized. The result is a closed-form efficient algorithm using n processors, where n is the number of kinematic chains connecting the base to the end-effector. The dynamics computations are based on the Newton-Euler formalism. The parallel algorithm arises from a judicious choice of the coordinate frames attached to each of the legs, which allows the exploitation of the parallel nature of the mechanism itself. Examples of the application of the algorithm to a planar three-degree-of-freedom parallel manipulator and to a spatial six-degree-of-freedom parallel manipulator are presented.

scholarly journals Three Degree of Freedom Spatial Parallel Manipulator Inverse Kinematic Position Analysis

2018 ◽  
Vol 7 (4.5) ◽  
pp. 98
Author(s):  
Srinivasa Rao Pundru ◽  
Mohan Rao Nalluri
Keyword(s):  
Parallel Manipulator ◽  
Inverse Kinematic ◽  
Degree Of Freedom ◽  
Algebraic Equations ◽  
Position Analysis ◽  
Fixed Base ◽  
Rotational Joint ◽  
Kinematic Position ◽  
Moving Platform ◽  
Three Degree Of Freedom

This paper presents inverse kinematic position analysis of three degree of freedom spatial parallel manipulator, which has three similar kinematic closed loops. Each loop consist of an actuated sliding linkage- rotational joint and spherical joint. The actuated sliding linkage is coupled to inclined limb of fixed base platform and rotational joints are integrated to the linear sliding actuators. The limbs are connected from rotational joints to moving platform by spherical joints. The degree of freedom of a manipulator is obtained by spatial kutzbach criterion. The inverse kinematic position analysis problem solved by using closed loop technique is applied to 3-coupled trigonometric equations which are obtained with side and behaviour constraints of a parallel manipulator. By using MATLAB the three non-linear coupled algebraic equations are solved. The inverse kinematic position analysis procedure is used in the development process of spatial parallel manipulator. The part of kinematic analysis is used to check the required positions-orientations and after kinematic process the obtained positions-orientations of the moving platform of the developed spatial parallel manipulator.  

scholarly journals Acceleration Analysis of 3-DOF Planar Parallel Manipulators by Means of Screw Theory

2016 ◽  
Vol 45 (2) ◽  
pp. 89-95
Author(s):  
Soheil Zarkandi
Keyword(s):  
Parallel Manipulator ◽  
Screw Theory ◽  
Parallel Manipulators ◽  
Second Order ◽  
Degree Of Freedom ◽  
Planar Parallel Manipulator ◽  
Acceleration Analysis ◽  
Three Degree Of Freedom ◽  
Planar Parallel Manipulators

This paper deals with the second order kinematics of three degree-of-freedom (DOF) planar parallel manipulators. The simple and compact expressions are derived for both the inverse and forward acceleration analyses using screw theory. Moreover, as an example, a 3-DOF planar parallel manipulator is introduced and its kinematics is analyzed using the proposed method.

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.

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