Mobility Analysis of the 3-UPU Parallel Mechanism Assembled for a Pure Translational Motion

2002 ◽  
Vol 124 (2) ◽  
pp. 259-264 ◽  
Author(s):  
Raffaele Di Gregorio ◽  
Vincenzo Parenti-Castelli
Keyword(s):  
Path Planning ◽  
Parallel Mechanism ◽  
Translational Motion ◽  
Analytic Form ◽  
Geometric Interpretation ◽  
Parallel Mechanisms ◽  
Basic Information ◽  
Mobility Analysis ◽  
Singular Configurations ◽  
Translation Motion

The occurrence of singular configurations in parallel mechanisms must be avoided during motion since the actuators cannot control motion even in the neighborhood of these configurations. As a consequence, the knowledge of the singular configurations of the mechanism is important for control purposes, for singularity-free path planning, and also represents basic information for the synthesis of a desired mechanism workspace free from singularities. In this paper the mobility analysis of the 3-UPU parallel mechanism assembled for obtaining a pure translation motion of the output platform is performed and both translation and rotation singularity loci are presented in analytic form and their geometric interpretation is given.

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.

Type Synthesis of Parallel Mechanisms With Multiple Operation Modes

2006 ◽  
Author(s):  
Xianwen Kong ◽  
Cle´ment M. Gosselin ◽  
Pierre-Luc Richard
Keyword(s):  
Parallel Mechanism ◽  
Translational Motion ◽  
Parallel Mechanisms ◽  
Motion Pattern ◽  
Type Synthesis ◽  
Motion Patterns ◽  
Operation Modes ◽  
Multiple Operation ◽  
Spherical Motion ◽  
General Method

There are usually several motion patterns having the same DOF (degree of freedom). For example, planar motion, spherical motion, and spatial translation are motion patterns with 3-DOF. An f-DOF parallel mechanism with multiple operation modes is a parallel mechanism that can generate different motion patterns with f DOF. Up to now, no method has been proposed for the type synthesis of parallel mechanisms with multiple operation modes. This paper presents a general method for the type synthesis of parallel mechanisms with multiple operation modes. Using the proposed approach, 3-DOF parallel mechanisms with both spherical and translational modes, i.e., parallel mechanisms generating both the spherical motion pattern and the spatial translational motion pattern, are generated systematically. A large number of parallel mechanisms with both spherical and translational modes are obtained.

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.

Constraint and Singularity Analysis of the Exechon Tripod

2012 ◽  
Author(s):  
Dimiter Zlatanov ◽  
Matteo Zoppi ◽  
Rezia Molfino
Keyword(s):  
Machine Tool ◽  
System Approach ◽  
Parallel Mechanism ◽  
Singularity Analysis ◽  
Geometric Interpretation ◽  
End Effector ◽  
Singular Configurations ◽  
Parallel Kinematic ◽  
Three Degree Of Freedom ◽  
Fixture System

The paper discusses mobility and singularities of the Exechon three-degree-of-freedom (dof) parallel mechanism (PM) on which a family of parallel kinematic machines is based. Exechon designs are used by a number of machine-tool makers. A new version of the manipulator has been developed as a component of a mobile self-reconfigurable fixture system within an inter-European project. The PM has two UPR (4-dof) legs, constrained to move in a common rotating plane, and an SPR (5-dof) leg. The paper focuses on the constraint and singularity analysis of the mechanism. The screw systems of end-effector freedoms and constraints are identified. The singular configurations are classified in detail and their geometric interpretation is discussed. The velocity kinematics and the Jacobian operator are formulated via a screw-system approach. A fully parameterized package of Maple tools has been developed and used to visualize singularities and their consequences.

Kinematically Redundant Planar Parallel Mechanisms for Optimal Singularity Avoidance

2017 ◽  
Vol 139 (4) ◽  
Author(s):  
Mats Isaksson
Keyword(s):  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Power Transmission ◽  
Load Capacity ◽  
Parallel Mechanisms ◽  
Kinematic Redundancy ◽  
Singularity Avoidance ◽  
Cycle Times ◽  
Singular Configurations ◽  
Redundant Mechanism

A parallel mechanism possesses several advantages compared to a similar-sized serial mechanism, including the potential for higher accuracy and reduced moving mass, the latter enabling increased load capacity and higher acceleration. One of the most important issues affecting a parallel mechanism is the potential of parallel singularities. Such configurations strongly affect the performance of a parallel mechanism, both in the actual singularity and in its vicinity. For example, both the stiffness of a mechanism and the efficiency of the power transmission to the tool platform are related to the closeness to singular configurations. A mechanism with a mobility larger than the mobility of its tool platform is referred to as a kinematically redundant mechanism. It is well known that introducing kinematic redundancy enables a mechanism to avoid singular configurations. In this paper, three novel kinematically redundant planar parallel mechanisms are proposed. All three mechanisms provide planar translations of the tool platform in two degrees-of-freedom, in addition to infinite rotation of the platform around an axis normal to the plane of the translations. The unique feature of the proposed mechanisms is that, with the appropriate inverse kinematics solutions, all configurations in the entire workspace feature optimal singularity avoidance. It is demonstrated how it is sufficient to employ five actuators to achieve this purpose. In addition, it is shown how including more than five actuators significantly reduces the required actuator motions for identical motions of the tool platform, thereby reducing the cycle times for typical applications.

scholarly journals Positioning Accuracy Analysis of the Parallel Mechanism Near Singular Positions

2015 ◽  
Vol 20 (1) ◽  
pp. 5-18 ◽  
Author(s):  
J. Bałchanowski
Keyword(s):  
Numerical Modelling ◽  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Accuracy Analysis ◽  
Parallel Mechanisms ◽  
Contact Interactions ◽  
Positioning Accuracy ◽  
Singular Configurations ◽  
Positioning Errors ◽  
Three Degrees Of Freedom

Abstract This paper presents a method of numerical modelling of parallel mechanisms with clearances in their kinematic pairs taken into account. The pairs with clearances are modelled as shape connections based on constraints in the form of contact interactions. Using the created models simulations were run to determine the positioning errors of the links in a parallel mechanism with three degrees of freedom (MR2120). In particular, the accuracy of positioning the links close to the mechanism singular configurations was studied.

Mobility and Workspace of a 3-5R Translational Parallel Mechanism

2006 ◽  
Author(s):  
Syamsul Huda ◽  
Yukio Takeda
Keyword(s):  
Parallel Mechanism ◽  
Screw Theory ◽  
Translational Motion ◽  
Numerical Calculations ◽  
Mobility Analysis ◽  
Spatial Mechanism ◽  
Size And Shape

A study about mobility and workspace of a 3-5R translational parallel spatial mechanism that has three symmetric limbs is presented. Mobility analysis based on the screw theory and numerical calculations were carried out to show if the proposed mechanism enabled the pure translational motion of a platform. The size and shape of workspace of the mechanism were also evaluated.

Singularity Analysis of Large Workspace 3RRRS Parallel Mechanism Using Line Geometry and Linear Complex Approximation

2010 ◽  
Vol 3 (1) ◽  
Author(s):  
Alon Wolf ◽  
Daniel Glozman
Keyword(s):  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Screw Theory ◽  
Singularity Analysis ◽  
Community Research ◽  
Parallel Mechanisms ◽  
Line Geometry ◽  
Equilibrium Equations ◽  
Six Degrees Of Freedom ◽  
Singular Configurations

During the last 15 years, parallel mechanisms (robots) have become more and more popular among the robotics and mechanism community. Research done in this field revealed the significant advantage of these mechanisms for several specific tasks, such as those that require high rigidity, low inertia of the mechanism, and/or high accuracy. Consequently, parallel mechanisms have been widely investigated in the last few years. There are tens of proposed structures for parallel mechanisms, with some capable of six degrees of freedom and some less (normally three degrees of freedom). One of the major drawbacks of parallel mechanisms is their relatively limited workspace and their behavior near or at singular configurations. In this paper, we analyze the kinematics of a new architecture for a six degrees of freedom parallel mechanism composed of three identical kinematic limbs: revolute-revolute-revolute-spherical. We solve the inverse and show the forward kinematics of the mechanism and then use the screw theory to develop the Jacobian matrix of the manipulator. We demonstrate how to use screw and line geometry tools for the singularity analysis of the mechanism. Both Jacobian matrices developed by using screw theory and static equilibrium equations are similar. Forward and inverse kinematic solutions are given and solved, and the singularity map of the mechanism was generated. We then demonstrate and analyze three representative singular configurations of the mechanism. Finally, we generate the singularity-free workspace of the mechanism.

On the Design of Singularity-Free Cable-Driven Parallel Mechanism Based on Grassmann Geometry

2012 ◽  
Author(s):  
Yu Zou ◽  
Yuru Zhang ◽  
Yaojun Zhang
Keyword(s):  
Parallel Mechanism ◽  
Jacobian Matrix ◽  
Singularity Analysis ◽  
Geometric Meaning ◽  
Parallel Mechanisms ◽  
Line Geometry ◽  
Singular Configurations ◽  
Negative Effect ◽  
Grassmann Line Geometry ◽  
Grassmann Geometry

This paper deals with the design of singularity-free cable-driven parallel mechanism. Due to the negative effect on the performance, singularities should be avoided in the design. The singular configurations of mechanisms can be numerically determined by calculating the rank of its Jacobian matrix. However, this method is inefficient and non-intuitive. In this paper, we investigate the singularities of planar and spatial cable-driven parallel mechanisms using Grassmann line geometry. Considering cables as line vectors in projective space, the singularity conditions are identified with clear geometric meaning which results in useful method for singularity analysis of the cable-driven parallel mechanisms. The method is applied to 3-DOF planar and 6-DOF spatial cable-driven mechanisms to determine their singular configurations. The results show that the singularities of both mechanisms can be eliminated by changing the dimensions of the mechanisms or adding extra cables.

scholarly journals A Double-Layered Elbow Exoskeleton Interface With 3-PRR Planar Parallel Mechanism for Axis Self-Alignment

2020 ◽  
Vol 13 (1) ◽  
Author(s):  
Mohammad I. Awad ◽  
Irfan Hussain ◽  
Shramana Ghosh ◽  
Yahya Zweiri ◽  
Dongming Gan
Keyword(s):  
Parallel Mechanism ◽  
Translational Motion ◽  
Orientation Angle ◽  
Frontal Plane ◽  
Vertex Angle ◽  
Parallel Mechanisms ◽  
Tissue Elasticity ◽  
Compact Size ◽  
Axis Alignment ◽  
Alignment Problem

Abstract Designing a mechanism for elbow self-axis alignment requires the elimination of undesirable joint motion and tissue elasticity. The novelty of this work lies in proposing a double-layered interface using a 3-PRR planar parallel mechanism as a solution to the axis alignment problem. 3-PRR planar parallel mechanisms are suitable candidates to solve this as they can span the desired workspace in a relatively compact size. In this paper, we present the modeling, design, prototyping, and validation of the double-layered elbow exoskeleton interface for axis self-alignment. The desired workspace for the self-axis alignment mechanism is specified based on the estimated maximum possible misalignment between the exoskeleton joint and the human anatomical elbow joint. Kinematic parameters of the 3-PRR planar mechanism are identified by formulating an optimization problem. The goal is to find the smallest mechanism that can span the specified workspace. The orientation angle of the mechanism’s plane addresses the frontal frustum vertex angle of the elbow’s joint, while the translational motion allows the translational offsets between the user’s elbow and the exoskeleton joint. The designed exoskeleton axis can passively rotate around the frontal plane ±15 deg and translate along the workspace 30 mm in the frontal plane. Experimental results (quantitative and qualitative) confirmed the capability of the proposed exoskeleton in addressing the complex elbow motion, user’s satisfaction, and ergonomics.

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