Modeling and Analysis of Parallel Mechanisms With Both Kinematic and Actuation Redundancies Via Screw Theory

2017 ◽  
Vol 9 (6) ◽  
Author(s):  
Long Kang ◽  
Wheekuk Kim ◽  
Byung-Ju Yi
Keyword(s):  
Screw Theory ◽  
Parallel Manipulators ◽  
Static Force ◽  
Parallel Mechanisms ◽  
Kinematic Redundancy ◽  
Mobility Analysis ◽  
Modeling And Analysis ◽  
Actuation Redundancy ◽  
Force Relationship

Two kinds of mechanical redundancies, namely kinematic redundancy and actuation redundancy, have been extensively studied due to their advantageous features in autonomous industry. Screw theory has been successfully applied to develop an analytical Jacobian of nonredundant parallel manipulators (PMs). However, to the best of our knowledge, screw theory has not been attempted for modeling of PMs with kinematic redundancies. Thus, first, through the mobility analysis of a simple nonredundant planar PM and its variations, this paper reviews kinematic and actuation redundancy systematically. Then, we demonstrated how to derive analytical Jacobian and also static force relationship for a PM with both kinematic and actuation redundancies by using the screw theory. Finally, simulations were performed to demonstrate the advantageous features of kinematic and actuation redundancies.

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.

A Simple Method for Mobility Analysis Using Reciprocal Screws

2006 ◽  
Author(s):  
Z. Huang ◽  
Q. J. Ge
Keyword(s):  
Coordinate System ◽  
Scalar Product ◽  
Simple Procedure ◽  
Parallel Manipulators ◽  
Simple Expression ◽  
Parallel Mechanisms ◽  
Complex Mechanism ◽  
Mobility Analysis ◽  
Simple Method ◽  
Analysis Process

The goal of this paper is to demonstrate that the Modified Gru¨bler-Kutzbach Criterion when combined with a simple procedure for determining the reciprocal screws offers a direct and simple method for analysing highly complex mechanisms including the over-constrained parallel manipulators. Since the scalar product of screws is not dependent on the choice of the origin, one can quickly obtain a simple expression of screws by selecting an appropriate coordinate system. In such simple expression, the coordinates of a screw would include 0 or 1, and thus greatly simplifies the procedure for determine the number of constraints in a mechanism. Seven rules have been presented to help simplify the analysis process. The advocated approach makes it possible to determine, within minutes, the mobility of a highly complex mechanism by using a pencil and a paper. Many over-constrained mechanisms, including three parallel mechanisms, are presented as examples.

scholarly journals Mobility analysis of parallel mechanisms based on screw theory and mechanism topology

2015 ◽  
Vol 7 (11) ◽  
pp. 168781401561046 ◽  
Author(s):  
Liping Wang ◽  
Huayang Xu ◽  
Liwen Guan
Keyword(s):  
Screw Theory ◽  
Parallel Mechanisms ◽  
Mobility Analysis

Synthesis of 2T1R Decoupled Parallel Manipulators

2011 ◽  
Vol 308-310 ◽  
pp. 2025-2030 ◽  
Author(s):  
Wen Juan Lu ◽  
Li Jie Zhang ◽  
Da Xing Zeng ◽  
Ruo Song Wang
Keyword(s):  
Screw Theory ◽  
Control Design ◽  
Parallel Manipulators ◽  
Parallel Mechanisms ◽  
Type Synthesis ◽  
Precision Control ◽  
Kinematic Chains ◽  
Step Procedure ◽  
Nonlinear Relation ◽  
Three Degree Of Freedom

For the general parallel mechanisms(PMS), since the coupling between kinematic chains, the nonlinear relation between the input and output is presented, which have led to difficulty in the trajectory planning and precision control. Design of motion decoupled parallel mechanisms(DPMS) has become a good new topic in this area and has captured researcher's attention. In this work, the approach to a synthesis of three degree-of-freedom(3-DOF) DPMS is considered based on screw theory and motion synthesis ideas. Criterions for type synthesis of the branches for DPMS is established according to the twist screw system of the limbs, which assures the decoupling in each limb. Then a six-step procedure is presented for the type synthesis of 2T1R decoupled mechanisms.

Enumeration and instantaneous mobility analysis of a class of 3-UPU parallel manipulators with equilateral triangular platforms

Robotica ◽  
2021 ◽  
pp. 1-32
Author(s):  
Sercan Boztaş ◽  
Gökhan Kiper
Keyword(s):  
Software Package ◽  
Degrees Of Freedom ◽  
Screw Theory ◽  
Parallel Manipulators ◽  
Mobility Analysis ◽  
Specific Design ◽  
Design Task ◽  
Moving Platforms ◽  
Joint Axis ◽  
Motion Characteristics

Abstract In this study, several joint axis orientations on equilateral platforms and the limbs of 3-UPU parallel manipulators (PMs) are examined. The generated joint layouts for the platforms were matched with each other to generate and enumerate manipulator architectures based on certain assumptions. The structures of thus obtained manipulators are examined and limb types were determined. These limb types were analyzed using screw theory. The instantaneous mobility of the manipulators and the motion characteristics of the moving platforms are tabulated. The finite mobility analysis of one of the manipulators is performed using a software package as an example. Among several different 3-UPU PM architectures, 118 novel 3-UPU PMs with non-parasitic 3-degrees-of-freedom are significantly important. The classified 3-UPU PMs with determined motion characteristics can be used by researchers as a design alternative for their specific design task.

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.

Geometric synthesis of spatial parallel manipulators with fewer than six degrees of freedom

2002 ◽  
Vol 216 (12) ◽  
pp. 1175-1185 ◽  
Author(s):  
T S Zhao ◽  
J S Dai ◽  
Z Huang
Keyword(s):  
Mechanism Design ◽  
Degrees Of Freedom ◽  
Screw Theory ◽  
Algebraic Approach ◽  
Structural Complexity ◽  
Parallel Manipulators ◽  
Parallel Mechanisms ◽  
Kinematic Pair ◽  
Type Synthesis ◽  
Six Degrees Of Freedom

Manipulators with fewer than six degrees of freedom meet specific tasks and have the advantage of reducing structural complexity, design redundancy and cost. In order to construct parallel manipulators for given tasks, this paper develops an algebraic approach to type synthesis of spatial parallel mechanisms with fewer than six degrees of freedom based on the screw theory. With the proposed steps (i.e. describing restraining screws, identifying basic kinematic pair (KP) screws reciprocal to the restraining screws, linearly transforming the basic KP screws to obtain equivalent serial limbs and allocating the serial limbs) new parallel mechanisms can be constructed. The approach converts a mechanism design into a screw algebra operation, in which screws describe kinematic pairs and constraints between links. As examples, synthesis procedures of parallel mechanisms with four degrees of freedom are given, from which five novel parallel mechanisms result.

On the terminology and geometric aspects of redundant parallel manipulators

Robotica ◽  
2012 ◽  
Vol 31 (1) ◽  
pp. 137-147 ◽  
Author(s):  
Andreas Müller
Keyword(s):  
Vector Fields ◽  
Kinematic Model ◽  
Parallel Manipulators ◽  
Redundant Actuation ◽  
Parallel Kinematics ◽  
Kinematic Redundancy ◽  
Control Vector ◽  
Serial Manipulators ◽  
Actuation Redundancy ◽  
Parallel Kinematics Machines

SUMMARYParallel kinematics machines (PKMs) can exhibit kinematics as well as actuation redundancy. While the meaning of kinematic redundancy has been already clarified for serial manipulators, actuation redundancy, which is only possible in PKMs, is differently classified in the literature. In this paper a consistent terminology for general redundant PKM is proposed. A kinematic model is introduced with the configuration space (c-space) as central part. The notion of kinematic redundancy is recalled for PKM. C-space, output, and input singularities are distinguished. The significance of the c-space geometry is emphasized, and it is pointed out geometrically that input singularities can be avoided by redundant actuation schemes. In order to distinguish different actuation schemes of PKM, a nonlinear control system is introduced whose dynamics evolves on c-space. The degree of actuation (DOA) is introduced as the number of independent control vector fields, and PKMs are classified as full-actuated and underactuated machines. Relating this DOA to degree of freedom allows to classify the actuation redundancy.

Mobility Analysis of Parallel Mechanisms Based on Screw Theory and the Concept of Equivalent Serial Kinematic Chain

2005 ◽  
Author(s):  
Xianwen Kong ◽  
Cle´ment M. Gosselin
Keyword(s):  
Systematic Approach ◽  
Screw Theory ◽  
Kinematic Chain ◽  
Second Step ◽  
Parallel Mechanisms ◽  
Mobility Analysis ◽  
Single Loop ◽  
Kinematic Chains ◽  
Serial Chain ◽  
Parallel Kinematic

This paper presents a systematic approach for the mobility analysis of parallel mechanisms. The method is based on screw theory and the concept of equivalent serial chain. An equivalent serial kinematic chain of a k-legged PKC (parallel kinematic chain) is defined as a serial kinematic chain which has the same twist system and the wrench system as the k-legged PKC. Using the proposed approach, the mobility analysis of a PKC is performed in two steps. The first step is the instantaneous mobility analysis, and the second step is the full-cycle mobility inspection. The first step is dealt with based on screw theory. The second step is performed with the aid of the concept of equivalent serial chain and the types of multi-DOF overconstrained single-loop kinematic chains. The proposed approach is illustrated with several examples.

Synthesis of Two-Degree-of-Freedom Rotational Decoupled Manipulators of a 2R-Type Branch

2013 ◽  
Vol 284-287 ◽  
pp. 1929-1935
Author(s):  
Da Xing Zeng ◽  
Wen Juan Lu ◽  
Li Jie Zhang ◽  
Yi Tong Zhang
Keyword(s):  
Trajectory Planning ◽  
Screw Theory ◽  
Parallel Manipulators ◽  
Parallel Mechanisms ◽  
Type Synthesis ◽  
Precision Control ◽  
Kinematic Chains ◽  
Parallel Kinematic ◽  
Branch Type ◽  
Two Degree Of Freedom

Strong coupling is one of the prominent features of the general parallel mechanisms(Par. Mec.), which has led to difficulty in the trajectory planning and precision control. To solve this problem, the designing of motion decoupled parallel mechanisms(Dec. Par. Mec.) has become a hot topic. This paper, based on the work achieved in our pre-papers, is to make an improvement on the criterion for a branch type synthesis of the rotational decoupled parallel mechanisms(Rot. Dec. Par. Mec.), which ensures the decoupling of the rotations in each limb. This paper focuses on a type synthesis of the decoupled parallel mechanisms with two degree of freedoms (DOFs). Decoupled parallel manipulators with two parallel kinematic chains, one of which is of type 2R(R represents rotation), are taken into consideration in this paper. A large number of novel decoupled architectures are already obtained, some of which have got an application for a China Patent. What has been done in this paper is carried out by means of the screw theory, which has effectively avoided complex equations by synthesis.

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