Mobility of Overconstrained Parallel Mechanisms

2004 ◽  
Vol 128 (1) ◽  
pp. 220-229 ◽  
Author(s):  
Jian S. Dai ◽  
Zhen Huang ◽  
Harvey Lipkin
Keyword(s):  
Physical Properties ◽  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
General Mechanism ◽  
Parallel Mechanisms ◽  
Mobility Analysis ◽  
New Approach ◽  
Redundant Constraints ◽  
Overconstrained Mechanisms ◽  
System Characteristics

The Kutzbach–Grübler mobility criterion calculates the degrees of freedom of a general mechanism. However, the criterion can break down for mechanisms with special geometries, and in particular, the class of so-called overconstrained parallel mechanisms. The problem is that the criterion treats all constraints as active, even redundant constraints, which do not affect the mechanism degrees of freedom. In this paper we reveal a number of screw systems of a parallel mechanism, explore their inter-relationship and develop an original theoretical framework to relate these screw systems to motion and constraints of a parallel mechanism to identify the platform constraints, mechanism constraints and redundant constraints. The screw system characteristics and relationships are investigated for physical properties and a new approach to mobility analysis is proposed based on decompositions of motion and constraint screw systems. New versions of the mobility criterion are thus presented to eliminate the redundant constraints and accurately predict the platform degrees of freedom. Several examples of overconstrained mechanisms from the literature illustrate the results.

Screw System Analysis of Parallel Mechanisms and Applications to Constraint and Mobility Study

2004 ◽  
Author(s):  
Jian S. Dai ◽  
Zhen Huang ◽  
Harvey Lipkin
Keyword(s):  
Degrees Of Freedom ◽  
System Analysis ◽  
General Mechanism ◽  
Parallel Mechanisms ◽  
Mobility Analysis ◽  
New Approach ◽  
Redundant Constraints ◽  
Overconstrained Mechanisms ◽  
Mobility Study ◽  
System Characteristics

The Kutzbach-Gru¨bler mobility criterion calculates the degrees-of-freedom of a general mechanism. However, the criterion can break down for mechanisms with special geometries, and in particular, the class of so-called overconstrained mechanisms. The problem is that the criterion treats all constraints as active, even redundant constraints, which do not affect the mechanism degrees-of-freedom. This paper examines the screw systems of a parallel mechanism to identify the redundant constraints. The screw system characteristics and relationships are then investigated for physical properties. Then a new approach to mobility analysis is proposed based on screw system decompositions. A new version of the mobility criterion is presented to eliminate the redundant constraints and correctly predict the platform degrees-of-freedom. Several examples of overconstrained mechanisms from the literature illustrate the results.

Mobility Analysis of a Novel 3-5R Parallel Mechanism Family

2004 ◽  
Vol 126 (1) ◽  
pp. 79-82 ◽  
Author(s):  
Q. C. Li ◽  
Z. Huang
Keyword(s):  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Screw Theory ◽  
Kinematic Chain ◽  
Parallel Mechanisms ◽  
Mobility Analysis

Mobility analysis of a novel 3-5R parallel mechanism family whose limb consists of a 2R and a 3R parallel subchain is performed by the aid of screw theory. A mobility criterion applicable to such 3-leg parallel mechanisms in which each kinematic chain contains five kinematic pairs is proposed. It is shown that under different structural conditions, the 3-5R parallel mechanism can have 3, 4, or 5 DOF (degrees of freedom). The structural conditions that guarantee the full-cycle mobility are analyzed. The analysis and the method presented in this paper will be helpful in using such a 3-5R parallel mechanism family and introduce new insights into the mobility analysis of parallel mechanisms.

scholarly journals A New Approach of Soft Joint Based on a Cable-Driven Parallel Mechanism for Robotic Applications

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1468
Author(s):  
Luis Nagua ◽  
Carlos Relaño ◽  
Concepción A. Monje ◽  
Carlos Balaguer
Keyword(s):  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Kinematic Model ◽  
Experimental Tests ◽  
Humanoid Robots ◽  
Inverse Kinematic ◽  
Element Analysis ◽  
New Approach ◽  
Flexible Polymer ◽  
The Mathematical Model

A soft joint has been designed and modeled to perform as a robotic joint with 2 Degrees of Freedom (DOF) (inclination and orientation). The joint actuation is based on a Cable-Driven Parallel Mechanism (CDPM). To study its performance in more detail, a test platform has been developed using components that can be manufactured in a 3D printer using a flexible polymer. The mathematical model of the kinematics of the soft joint is developed, which includes a blocking mechanism and the morphology workspace. The model is validated using Finite Element Analysis (FEA) (CAD software). Experimental tests are performed to validate the inverse kinematic model and to show the potential use of the prototype in robotic platforms such as manipulators and humanoid robots.

Design of a Four Legged Parallel Mechanism to Improve the Dexterity of Walking Robot

2009 ◽  
Author(s):  
ChiHyo Kim ◽  
KunWoo Park ◽  
TaeSung Kim ◽  
MinKi Lee
Keyword(s):  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Jacobian Matrix ◽  
Topology Design ◽  
Condition Numbers ◽  
Walking Robots ◽  
Rough Terrain ◽  
Parallel Mechanisms ◽  
Walking Robot ◽  
Intermediate Mechanism

This paper designs a four legged parallel mechanism to improve the dexterity of three layered parallel walking robot. Topology design is conducted for a leg mechanism composed of four legs, base and ground, which constitute a redundant parallel mechanism. This mechanism is subdivided into four sub-mechanism composed of three legs. A motor vector is adopted to determine the 6×8 Jacobian of the redundant parallel mechanism and the 6×6 Jacobian of the sub-mechanisms, respectively. The condition number of the Jacobian matrix is used as an index to measure a dexterity. We analyze the condition numbers of the Jacobian over the positional and orientational walking space. The analytical results show that a sub-mechanism has lots of singularities within workspace but they are removed by a redundant parallel mechanism improving the dexterity. This paper presents a parallel typed walking robot to enlarge walking space and stability region. Seven types of three layered walking robots are designed by inserting an intermediate mechanism between the upper and the lower legged parallel mechanisms. They provide various types of gaits to walk rough terrain and climb over a wall with small degrees of freedom.

scholarly journals Reconfiguration Analysis of a 3-DOF Parallel Mechanism

Robotics ◽  
2019 ◽  
Vol 8 (3) ◽  
pp. 66
Author(s):  
Maurizio Ruggiu ◽  
Xianwen Kong
Keyword(s):  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Operation Mode ◽  
Parallel Mechanisms ◽  
Universal Joint ◽  
Kinematic Chains ◽  
Constraint Equations ◽  
The Third ◽  
Equilateral Triangles ◽  
Moving Platform

This paper deals with the reconfiguration analysis of a 3-DOF (degrees-of-freedom) parallel manipulator (PM) which belongs to the cylindrical parallel mechanisms family. The PM is composed of a base and a moving platform shaped as equilateral triangles connected by three serial kinematic chains (legs). Two legs are composed of two universal (U) joints connected by a prismatic (P) joint. The third leg is composed of a revolute (R) joint connected to the base, a prismatic joint and universal joint in sequence. A set of constraint equations of the 1-RPU−2-UPU PM is derived and solved in terms of the Euler parameter quaternion (a.k.a. Euler-Rodrigues quaternion) representing the orientation of the moving platform and of the Cartesian coordinates of the reference point on the moving platform. It is found that the PM may undergo either the 3-DOF PPR or the 3-DOF planar operation mode only when the base and the moving platform are identical. The transition configuration between the operation modes is also identified.

Kinematics and Workspace Analysis of 3-RPP Parallel Mechanism

2013 ◽  
Vol 456 ◽  
pp. 146-150
Author(s):  
Zhi Jiang Xie ◽  
Jun Zhang ◽  
Xiao Bo Liu
Keyword(s):  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Parallel Mechanisms ◽  
Vector Method ◽  
Workspace Analysis ◽  
Inverse Solutions ◽  
Three Degrees Of Freedom

This paper designed a kind of parallel mechanism with three degrees of freedom, the freedom and movement types of the robot are analyzed in detail, the parallel mechanisms Kinematics positive and inverse solutions are derived through using the vector method. And at last its workspace is analyzed and studied systematically.

Jacobian Derivation of 5-DOF 3R2T Parallel Mechanisms

2004 ◽  
Author(s):  
Qinchuan Li ◽  
Xudong Hu ◽  
Zhen Huang
Keyword(s):  
Degrees Of Freedom ◽  
Jacobian Matrix ◽  
Screw Theory ◽  
Kinematic Chain ◽  
Parallel Mechanisms ◽  
Mobility Analysis

This paper presents a method for the Jacobian derivation of 5-DOF 3R2T PMs (parallel mechanisms), where 3R denotes three rotational DOFs (degrees of freedom) and 2T denotes two translational DOFs. First the mobility analysis of such kind of parallel mechanisms is reviewed briefly. The Jacobian matrix of the single limb kinematic chain is obtained via screw theory, which is a 6 × 5 matrix. Then it is shown that the mobility analysis of such kind of PM is important when simplifying the 6 × 5 matrix into a 5 × 5 Jacobian matrix. After obtaining the 5 × 5 Jacobian matrix for each limb, a 5 × 5 Jacobian matrix for the whole mechanism can be established.

Redundant Parallel Mechanism for Haptic Applications

2010 ◽  
Vol 4 (4) ◽  
pp. 338-345 ◽  
Author(s):  
Jumpei Arata ◽  
◽  
Hideo Fujimoto
Keyword(s):  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Display Device ◽  
Parallel Mechanisms ◽  
Prototype Implementation ◽  
Haptic Devices ◽  
Multiple Degrees Of Freedom ◽  
High Rigidity ◽  
Wide Range ◽  
Fixed Base

With haptic devices becoming increasingly common in both industrial field and consumer use, parallel mechanisms have been widely introduced for their high rigidity, output, accuracy and high backdrivability due to their multi-legged structure and fixed base actuators. In general parallel mechanism, redundancy enlarges the working area and avoids singularity. The redundant parallel mechanism we present introduces these advantages into haptic applications. Introducing this mechanism into a multiple degrees-of-freedom (DOF) structure realizes a wide range of working areas in rotation. The redundant parallel mechanism implemented in translational force display device, and multi-DOF force display device demonstrate the advantages of the redundant parallel mechanism in haptic applications. Following an overview, we introduce the prototype implementation and evaluation of these devices and discuss the effectiveness of the redundant parallel mechanism in haptic applications.

Mobility Change in Two Types of Metamorphic Parallel Mechanisms

2009 ◽  
Vol 1 (4) ◽  
Author(s):  
Dongming Gan ◽  
Jian S. Dai ◽  
Qizheng Liao
Keyword(s):  
Parallel Mechanism ◽  
Type A ◽  
Parallel Mechanisms ◽  
Mobility Analysis ◽  
Topological Change ◽  
Mobility Factor ◽  
Local Mobility

This paper presents a new joint coined as the rT joint and proposes two types of metamorphic parallel mechanisms assembled with this rT joint. In the first type, the mechanism changes its topology by turning the rT joints in all limbs into different configurations. This change in mobility is completed by two cases illustrated by a 3(rT)PS metamorphic parallel mechanism having variable mobility from 3 to 6 and a 3(rT)P(rT) parallel mechanism having various configurations including pure translations, pure rotations, and mobility 4. In the second type, a central strut with the rT joint is added in a parallel mechanism. The variable mobility of the mechanism results from the topological change of the central (rT)P(rT) strut. This is illustrated in a 3SPS-1(rT)P(rT) metamorphic parallel mechanism, which changes its mobility from 4 to 5. It is demonstrated in mobility analysis that the change in local mobility of each limb results in the change in the platform mobility that a metamorphic process can be achieved. This particular analysis leads to advancement of improved Grübler–Kutzbach criterion by introducing the local mobility factor in the mobility analysis.

scholarly journals Synthesis method of two translational compliant mechanisms with redundant actuation

2021 ◽  
Vol 12 (2) ◽  
pp. 983-995
Author(s):  
Shihua Li ◽  
Yajie Zhou ◽  
Yanxia Shan ◽  
Shuang Chen ◽  
Jinhan Han
Keyword(s):  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Compliant Mechanisms ◽  
Synthesis Method ◽  
Synthesis Process ◽  
Parallel Mechanisms ◽  
Synthesis Conditions ◽  
Compliant Parallel Mechanism ◽  
Atlas Method ◽  
Driving Stability

Abstract. In the fields of electronic packaging, micromanipulation, scanning, and two translational (2T) mechanisms are required, especially with high stiffness, for a large workspace, with good driving stability, and other occasions. Redundant actuators are required to improve the performance of the 2T compliant parallel mechanism. The novelty of the work is to propose a new method for the type synthesis of a 2T redundant actuated compliant parallel mechanism based on the freedom and constraint topology (FACT) approach and the atlas approach. The synthesis conditions are given, and the synthesis process is formulated. With this method, new 2T redundant actuated compliant parallel mechanisms are synthesized. Some new mechanisms have been synthesized, which enriches the compliant parallel mechanism configurations. Based on the atlas method, the synthesized mechanism is analyzed. The results verify the correctness and effective of the synthesis method. The method is also suitable for a type of synthesis of redundant actuated compliant parallel mechanisms with 3, 4, 5, and 6 degrees of freedom (DOF), respectively.

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