The Synthesis of Three-Degree-of-Freedom Planar Parallel Mechanisms with Revolute Joints (3-RRR) for an Optimal Singularity-Free Workspace

2004 ◽  
Vol 21 (5) ◽  
pp. 259-274 ◽  
Author(s):  
Marc Arsenault ◽  
Roger Boudreau
Keyword(s):  
Degree Of Freedom ◽  
Parallel Mechanisms ◽  
Revolute Joints ◽  
Three Degree Of Freedom

A 3-ṞPR Parallel Mechanism With Singularities That are Self-Motions

2010 ◽  
Vol 2 (3) ◽  
Author(s):  
Novona Rakotomanga ◽  
Ilian A. Bonev
Keyword(s):  
Parallel Mechanism ◽  
Control Strategies ◽  
Joint Space ◽  
Degree Of Freedom ◽  
Parallel Mechanisms ◽  
Active Joint ◽  
Cartesian Space ◽  
Three Degree Of Freedom

The Cartesian workspace of most three-degree-of-freedom parallel mechanisms is divided by Type 2 (also called parallel) singularity surfaces into several regions. Accessing more than one such region requires crossing a Type 2 singularity, which is risky and calls for sophisticated control strategies. Some mechanisms can still cross these Type 2 singularity surfaces through “holes” that represent Type 1 (also called serial) singularities only. However, what is even more desirable is if these Type 2 singularity surfaces were curves instead. Indeed, there exists at least one such parallel mechanism (the agile eye) and all of its singularities are self-motions. This paper presents another parallel mechanism, a planar one, whose singularities are self-motions. The singularities of this novel mechanism are studied in detail. While the Type 2 singularities in the Cartesian space still constitute a surface, they degenerate into lines in the active-joint space, which is the main result of this paper.

Synthesis and Design of Reactionless Three-Degree-of-Freedom Parallel Mechanisms

2004 ◽  
Vol 20 (2) ◽  
pp. 191-199 ◽  
Author(s):  
C.M. Gosselin ◽  
F. Vollmer ◽  
G. Cote ◽  
Y. Wu
Keyword(s):  
Degree Of Freedom ◽  
Parallel Mechanisms ◽  
Three Degree Of Freedom

scholarly journals Kinematic analysis of the X4 translational–rotational parallel robot

2018 ◽  
Vol 15 (5) ◽  
pp. 172988141880384 ◽  
Author(s):  
Stefan Staicu ◽  
Zhufeng Shao ◽  
Zhaokun Zhang ◽  
Xiaoqiang Tang ◽  
Liping Wang
Keyword(s):  
High Speed ◽  
Parallel Manipulators ◽  
Parallel Robot ◽  
Degree Of Freedom ◽  
Parallel Mechanisms ◽  
Kinematic Chains ◽  
Revolute Joints ◽  
Commercial Applications ◽  
Recursive Matrix ◽  
Singularity Locus

High-speed pick-and-place parallel manipulators have attracted considerable academic and industrial attention because of their numerous commercial applications. The X4 parallel robot was recently presented at Tsinghua University. This robot is a four-degree-of-freedom spatial parallel manipulator that consists of high-speed closed kinematic chains. Each of its limbs comprises an active pendulum and a passive parallelogram, which are connected to the end effector with other revolute joints. Kinematic issues of the X4 parallel robot, such as degree of freedom analysis, inverse kinematics, and singularity locus, are investigated in this study. Recursive matrix relations of kinematics are established, and expressions that determine the position, velocity, and acceleration of each robot element are developed. Finally, kinematic simulations of actuators and passive joints are conducted. The analysis and modeling methods illustrated in this study can be further applied to the kinematics research of other parallel mechanisms.

Type Synthesis of Three-Degree-of-Freedom Translational Compliant Parallel Mechanisms

2015 ◽  
Vol 7 (3) ◽  
Author(s):  
Cong Yue ◽  
Ying Zhang ◽  
Hai-Jun Su ◽  
Xianwen Kong
Keyword(s):  
Screw Theory ◽  
Rigid Bodies ◽  
Degree Of Freedom ◽  
Design Stage ◽  
Parallel Mechanisms ◽  
Type Synthesis ◽  
Geometric Conditions ◽  
Synthesis Procedure ◽  
Flexure Joints ◽  
Three Degree Of Freedom

In this paper, we apply screw theory to type synthesis of compliant parallel mechanisms (PMs) with translational degree-of-freedom (DOF). Compliant PMs are formed by a moving platform supported by three or more limbs each of which is a serial chain of flexure joints and rigid bodies. They achieve movement through the deformation of flexure joints and have been widely used in precision machinery. As an important task in the conceptual design stage, the goal of type synthesis is to determine the chain of each limb as well as their relationship when they are assembled in parallel for a prescribed motion pattern. In our approach, we study a category of commonly used flexure primitives and flexure elements whose freedom and constraint spaces are characterized by twists and wrenches in screw theory. Following the well-studied synthesis procedure for rigid body PMs, we propose a synthesis procedure for compliant PMs via screw theory. As an example, we demonstrate the procedure for synthesizing compliant PMs with three translational DOF. Tables of limbs, types, and geometric conditions for the assemblies of these limbs are presented. The paper provides a catalog of 3DOF translational compliant PM designs. At last, we developed finite element simulation to validate one of the synthesized designs.

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.

Forward Position Analysis of Two 3-R Robots Manipulating a Planar Linkage Payload

1995 ◽  
Vol 117 (2A) ◽  
pp. 292-297 ◽  
Author(s):  
G. R. Pennock ◽  
K. G. Mattson
Keyword(s):  
Closed Loop ◽  
Degree Of Freedom ◽  
Sixth Order ◽  
Position Analysis ◽  
Revolute Joints ◽  
Order Polynomial ◽  
Cooperating Robots ◽  
Position Problem ◽  
Three Degree Of Freedom ◽  
Insight Into

This paper presents the forward position analysis of two planar three degree-of-freedom robots, with all revolute joints, manipulating a single degree-of-freedom closed-loop linkage payload. Kinematic constraint relations are developed which provide geometric insight into the cooperating robot-payload system and are important in the control of the two robots. For illustrative purposes, the payload that is considered here is a planar four-bar linkage. The paper shows that the orientation of a specified link in the payload can be described by a sixth-order polynomial. This polynomial is an important contribution, not only to the kinematics of the cooperating robots, but to the multiple-input closed-loop nine-bar linkage formed by the two robots and the payload. The polynomial contains important information regarding the assembly configurations and the stationary configurations of the system. The paper shows that zero, two, four, or six assembly configurations are possible and that each configuration corresponds to a different circuit of the system. Graphical methods are utilized to provide geometric insight into the assembly and stationary configurations and to check the results obtained from the sixth-order polynomial. A numerical example is included which demonstrates the importance of the polynomial in solving the forward position problem, and in determining the number of assembly configurations.

The Synthesis of Planar Parallel Manipulators with a Genetic Algorithm

1999 ◽  
Vol 121 (4) ◽  
pp. 533-537 ◽  
Author(s):  
R. Boudreau ◽  
C. M. Gosselin
Keyword(s):  
Genetic Algorithm ◽  
Parallel Manipulators ◽  
Optimization Method ◽  
Degree Of Freedom ◽  
Natural Evolution ◽  
Revolute Joints ◽  
Prismatic Joints ◽  
Genetic Algorithm Approach ◽  
Three Degree Of Freedom ◽  
Planar Parallel Manipulators

This paper presents a genetic algorithm approach for the synthesis of planar three-degree-of-freedom parallel manipulators. A genetic algorithm is an optimization method inspired by natural evolution. As in nature, the fittest members of a population are given better chances of reproducing and transmitting part of their genetic heritage to the next generation. This leads to stronger and stronger generations which evolve towards the solution of the problem. For the applications studied here, the individuals in the population consist of the architectural parameters of the manipulators. The algorithm optimizes these parameters to obtain a workspace as close as possible to a prescribed working area. For each individual of the population, the geometric description of the workspace can be obtained. The algorithm then determines the intersection between the prescribed workspace and the actual workspace, and minimizes the area of the regions that do not intersect. The method is applied to two planar three-degree-of-freedom parallel manipulators, one with prismatic joints and one with revolute joints.

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