A screw theory approach to compute instantaneous rotation axes of indeterminate spherical linkages

2020 ◽  
pp. 1-41
Author(s):  
Juan Ignacio Valderrama-Rodríguez ◽  
José M. Rico ◽  
J. Jesús Cervantes-Sánchez
Keyword(s):  
Screw Theory ◽  
Theory Approach ◽  
Rotation Axes ◽  
Spherical Linkages

scholarly journals A Screw Theory Approach for the Type Synthesis of Compliant Mechanisms With Flexures

2009 ◽  
Author(s):  
Hai-Jun Su ◽  
Denis V. Dorozhkin ◽  
Judy M. Vance
Keyword(s):  
Compliant Mechanisms ◽  
Screw Theory ◽  
Compliant Mechanism ◽  
Computational Techniques ◽  
Theory Approach ◽  
Type Synthesis ◽  
Precision Engineering ◽  
Pattern Design ◽  
Design Constraint ◽  
Systematic Formulation

This paper presents a screw theory based approach for the type synthesis of compliant mechanisms with flexures. We provide a systematic formulation of the constraint-based approach which has been mainly developed by precision engineering experts in designing precision machines. The two fundamental concepts in the constraint-based approach, constraint and freedom, can be represented mathematically by a wrench and a twist in screw theory. For example, an ideal wire flexure applies a translational constraint which can be described a wrench of pure force. As a result, the design rules of the constraint-based approach can be systematically formulated in the format of screws and screw systems. Two major problems in compliant mechanism design, constraint pattern analysis and constraint pattern design are discussed with examples in details. This innovative method paves the way for introducing computational techniques into the constraint-based approach for the synthesis and analysis of compliant mechanisms.

Visual Measurement and Calibration of Geometric Errors of Rotating Axes for Five-axis Platform

2021 ◽  
Author(s):  
Song Yin ◽  
Haibo Zhou ◽  
Xia Ju ◽  
Zhiqiang Li
Keyword(s):  
Screw Theory ◽  
Coupling Mechanism ◽  
Geometric Errors ◽  
Visual Measurement ◽  
Decoupling Method ◽  
Vision Measurement ◽  
Rotation Axes ◽  
Error Terms ◽  
Error Calibration ◽  
Five Axis

Abstract In this paper, a method for identifying and decoupling geometric errors of rotation axes using vision measurement is proposed. Based on screw theory and exponential product formula, identification equations of position-dependent geometric errors (PDGEs) and position-independent geometric errors (PIGEs) of the rotation axes are established. The mapping relationships between the error twist and geometric errors are established. The error model provides the coupling mechanism of PDGEs and PIGEs. Furthermore, a progressive decoupling method is proposed to separate PDGEs and PIGEs without additional assumptions. The pose parameters, required for solving the identification equations, are obtained by visual measurement. Then, the error terms of PIGEs and PDGEs are determined. Lastly, the error calibration of the rotation axes is investigated, thus providing an average rotary table orientation error reduction of 28.1% compared to the situation before calibration.

Realizing Orthogonal Motions With Wire Flexures Connected in Parallel

2010 ◽  
Author(s):  
Hai-Jun Su ◽  
Hafez Tari
Keyword(s):  
Screw Theory ◽  
Theory Approach ◽  
Mobility Pattern ◽  
Simply Connected

In this paper, we study the synthesis of wire flexures to achieve orthogonal motion by using a recently developed screw theory based approach. For a given desired mobility pattern, our goal is to find a system of wire flexures that are simply connected in parallel between the functional stage and the ground. It has been shown that a wire flexure is essentially a pure force or a line screw. An n dof motion space (allowable motion) is realizable if its reciprocal constraint space can be spanned by 6 – n line screws or forces. We first enumerate all possible one to five degree of motion spaces that are formed by motions along the coordinate axes attached on the functional stage. For each of these 34 motion spaces, we apply the screw theory approach to find its reciprocal force space as well as its rank. We conclude that 18 of them are realizable, 4 are realizable only when their pitches have opposite signs and 12 are not realizable. For each of these 34 cases, we provide an example showing the maximum number of independent wire flexures.

scholarly journals A Screw Theory Approach for the Conceptual Design of Flexible Joints for Compliant Mechanisms

2009 ◽  
Vol 1 (4) ◽  
Author(s):  
Hai-Jun Su ◽  
Denis V. Dorozhkin ◽  
Judy M. Vance
Keyword(s):  
Compliant Mechanisms ◽  
Screw Theory ◽  
Compliant Mechanism ◽  
Computational Techniques ◽  
Theory Approach ◽  
Flexible Joints ◽  
Precision Engineering ◽  
Design Constraint ◽  
Analysis And Synthesis ◽  
Prismatic Joints

This paper presents a screw theory based approach for the analysis and synthesis of flexible joints using wire and sheet flexures. The focus is on designing flexure systems that have a simple geometry, i.e., a parallel constraint pattern. We provide a systematic formulation of the constraint-based approach, which has been mainly developed by precision engineering experts in designing precision machines. The two fundamental concepts in the constraint-based approach, constraint and freedom, can be represented mathematically by a wrench and a twist in screw theory. For example, an ideal wire flexure applies a translational constraint, which can be described by a wrench of pure force. As a result, the design rules of the constraint-based approach can be systematically formulated in the format of screws and screw systems. Two major problems in compliant mechanism design, constraint pattern analysis, and constraint pattern design are discussed with examples in details. Lastly, a case study is provided to demonstrate the application of this approach to the design of compliant prismatic joints. This innovative method paves the way for introducing computational techniques into the constraint-based approach for the synthesis and analysis of compliant mechanisms.

scholarly journals A Screw Theory Approach to Computing the Instantaneous Rotation Centers of Indeterminate Planar Linkages

Robotics ◽  
2021 ◽  
Vol 11 (1) ◽  
pp. 6
Author(s):  
Juan Ignacio Valderrama-Rodríguez ◽  
José M. Rico ◽  
J. Jesús Cervantes-Sánchez ◽  
Ricardo García-García
Keyword(s):  
Screw Theory ◽  
Bilinear Forms ◽  
Theory Approach ◽  
Algebraic Equations ◽  
Euclidean Group ◽  
Planar Mechanisms ◽  
New Approach ◽  
Planar Linkages ◽  
The 19Th Century

This paper presents a screw theory approach for the computation of the instantaneous rotation centers of indeterminate planar linkages. Since the end of the 19th century, the determination of the instantaneous rotation, or velocity centers of planar mechanisms has been an important topic in kinematics that has led to the well-known Aronhold–Kennedy theorem. At the beginning of the 20th century, it was found that there were planar mechanisms for which the application of the Aronhold–Kennedy theorem was unable to find all the instantaneous rotation centers (IRCs). These mechanisms were denominated complex or indeterminate. The beginning of this century saw a renewed interest in complex or indeterminate planar mechanisms. In this contribution, a new and simpler screw theory approach for the determination of indeterminate rotation centers of planar linkages is presented. The new approach provides a simpler method for setting up the equations. Furthermore, the algebraic equations to be solved are simpler than the ones published to date. The method is based on the systematic application of screw theory, isomorphic to the Lie algebra, se(3), of the Euclidean group, SE(3), and the invariant symmetric bilinear forms defined on se(3).

Variable Motion/Force Transmissibility of a Metamorphic Parallel Mechanism With Reconfigurable 3T and 3R Motion

2015 ◽  
Author(s):  
Dongming Gan ◽  
Jian S. Dai ◽  
Jorge Dias ◽  
Lakmal D. Seneviratne
Keyword(s):  
Parallel Mechanism ◽  
Jacobian Matrix ◽  
Screw Theory ◽  
Singularity Analysis ◽  
Design Parameters ◽  
Force Transmission ◽  
Pure Rotation ◽  
Rotation Axes ◽  
Potential Applications ◽  
Force Transmissibility

This paper presents a metamorphic parallel mechanism which can switch its motion between pure translation (3T) and pure rotation (3R) motion. This feature stems from a reconfigurable Hooke (rT) joint of which one of the rotation axes can be altered freely. More than that, based on the reconfiguration of the rT joint, workspace of both 3T and 3R motion can be tunable and the rotation center of the 3R motion can be controlled along a line perpendicular to the base plane. Kinematics analysis is presented based on the geometric constraint of the parallel mechanism covering both 3T and 3R motion. Following these screw theory based motion/force transmission equations are obtained and their characteristics are investigated and linked to the singularity analysis using Jacobian matrix. Motion/force transmission indices can be used to optimize basic design parameters of the metamorphic parallel mechanism. This provides reference of this mechanism for potential applications requiring 3T and 3R motion.

Variable Motion/Force Transmissibility of a Metamorphic Parallel Mechanism With Reconfigurable 3T and 3R Motion

2016 ◽  
Vol 8 (5) ◽  
Author(s):  
Dongming Gan ◽  
Jian S. Dai ◽  
Jorge Dias ◽  
Lakmal D. Seneviratne
Keyword(s):  
Parallel Mechanism ◽  
Screw Theory ◽  
Singularity Analysis ◽  
Geometric Constraints ◽  
Design Parameters ◽  
Force Transmission ◽  
Pure Rotation ◽  
Rotation Axes ◽  
Potential Applications ◽  
Force Transmissibility

This paper presents a metamorphic parallel mechanism (MPM) which can switch its motion between pure translation (3T) and pure rotation (3R). This feature stems from a reconfigurable Hooke (rT) joint of which one of the rotation axes can be altered freely. More than that, based on the reconfiguration of the rT joint, workspace of both 3T and 3R motion can be tunable, and the rotation center of the 3R motion can be controlled along a line perpendicular to the base plane. Kinematics analysis is presented based on the geometric constraints of the parallel mechanism covering both 3T and 3R motion. Following this, screw theory based motion/force transmission equations are obtained, and their characteristics are investigated and linked to the singularity analysis using Jacobian matrix. Motion/force transmission indices can be used to optimize basic design parameters of the MPM. This provides reference of this mechanism for potential applications requiring 3T and 3R motion.

Design and Analysis of a Novel Reconfigurable Parallel Manipulator with Kirigami-inspired Bennett Plano-Spherical Linkages and Angular Pouch Motors

2021 ◽  
pp. 1-23
Author(s):  
Ketao Zhang ◽  
Chen Liu
Keyword(s):  
Parallel Manipulator ◽  
Closed Loop ◽  
Screw Theory ◽  
Geometric Approach ◽  
Reconfigurable Mechanisms ◽  
Serial Chain ◽  
Bending Actuator ◽  
Creative Art ◽  
Spherical Linkages ◽  
Motion Characteristics

Abstract Drawing inspiration from kirigami, a creative art of papercutting, this paper first present a simple crease pattern of a kirigami model. In terms of artimimetics which bridges the origami/kirigami art and mechanisms, the kinematic equivalent, an overconstrained 6R linkage, is extracted from the kirigami model. In terms of screw theory, constraint singularity induced transitory position and distinct closed-loop motion branches of the 6R linkage is revealed. Using the Bennett plano-spherical linkage as a closed-loop subchain of kinematic limbs, this paper then introduce a new reconfigurable parallel manipulator with three hybrid kinematic limbs. Each limb of the manipulator consists of a Bennett plano-spherical linkage and a R(RR) serial chain. Using a geometric approach, the constraints exerted on the platform by the hybrid limb are explored by analysing the motion-screw systems of the equivalent serial kinematic limb corresponding to each motion branch of the closed-loop subchain. Motion characteristics in each motion branch of the parallel manipulator are revealed. Inspired by origami-folding and inflatable actuators for soft robotics, this paper further presents a new design of inflatable bending actuator for changing motion branches of reconfigurable mechanisms. The conceptual design of the actuator is verified with a prototype fabricated using adhesive fabric and further application in reconfiguring a 3D printed foldable Bennett plano-spherical linkage.

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