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.

Realizing Orthogonal Motions With Wire Flexures Connected in Parallel

2010 ◽  
Vol 132 (12) ◽  
Author(s):  
Hai-Jun Su ◽  
Hafez Tari
Keyword(s):  
Screw Theory ◽  
Degree Of Freedom ◽  
Design Approach ◽  
Theory Approach ◽  
Mobility Pattern ◽  
Type Synthesis ◽  
Simply Connected ◽  
Typical Design

In this paper, we study the type synthesis of wire flexures to achieve orthogonal motions by using a recently developed screw theory based design 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 degree-of-freedom (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 34 possible 1–5DOF 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. At last, a typical design is provided for each of these motion spaces.

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.

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).

scholarly journals Algorithmic approach to geometric solution of generalized Paden–Kahan subproblem and its extension

2018 ◽  
Vol 15 (1) ◽  
pp. 172988141875515 ◽  
Author(s):  
Igor Dimovski ◽  
Mirjana Trompeska ◽  
Samoil Samak ◽  
Vladimir Dukovski ◽  
Dijana Cvetkoska
Keyword(s):  
Inverse Kinematics ◽  
Necessary Conditions ◽  
Screw Theory ◽  
Robot Manipulator ◽  
Theory Approach ◽  
Coordinate Systems ◽  
Number Of Solutions ◽  
Algorithmic Approach ◽  
Coordinate Frames ◽  
Inverse Kinematics Problem

Kinematics as a science of geometry of motion describes motion by means of position, orientation, and their time derivatives. The focus of this article aims screw theory approach for the solution of inverse kinematics problem. The kinematic elements are mathematically assembled through screw theory by using only the base, tool, and workpiece coordinate systems—opposite to conventional Denavit–Hartenberg approach, where at least n + 1 coordinate frames are needed for a robot manipulator with n joints. The inverse kinematics solution in Denavit–Hartenberg convention is implicit. Instead, explicit solutions to inverse kinematics using the Paden–Kahan subproblems could be expressed. This article gives step-by-step application of geometric algorithm for the solution of all the cases of Paden–Kahan subproblem 2 and some extension of that subproblem based on subproblem 2. The algorithm described here covers all of the cases that can appear in the generalized subproblem 2 definition, which makes it applicable for multiple movement configurations. The extended subproblem is used to solve inverse kinematics of a manipulator that cannot be solved using only three basic Paden–Kahan subproblems, as they are originally formulated. Instead, here is provided solution for the case of three subsequent rotations, where last two axes are parallel and the first one does not lie in the same plane with neither of the other axes. Since the inverse kinematics problem may have no solution, unique solution, or many solutions, this article gives a thorough discussion about the necessary conditions for the existence and number of solutions.

Ab initio band theory approach to electron energy loss near edge structures

1988 ◽  
Vol 46 ◽  
pp. 506-507
Author(s):  
Xudong Weng ◽  
O.F. Sankey ◽  
Peter Rez
Keyword(s):  
Ab Initio ◽  
Local Density ◽  
Interpolation Method ◽  
Atomic Orbital ◽  
Plane Waves ◽  
Large Set ◽  
Theory Approach ◽  
Band Theory ◽  
Atomic Orbitals ◽  
Pseudopotential Calculations

Single electron band structure techniques have been applied successfully to the interpretation of the near edge structures of metals and other materials. Among various band theories, the linear combination of atomic orbital (LCAO) method is especially simple and interpretable. The commonly used empirical LCAO method is mainly an interpolation method, where the energies and wave functions of atomic orbitals are adjusted in order to fit experimental or more accurately determined electron states. To achieve better accuracy, the size of calculation has to be expanded, for example, to include excited states and more-distant-neighboring atoms. This tends to sacrifice the simplicity and interpretability of the method.In this paper. we adopt an ab initio scheme which incorporates the conceptual advantage of the LCAO method with the accuracy of ab initio pseudopotential calculations. The so called pscudo-atomic-orbitals (PAO's), computed from a free atom within the local-density approximation and the pseudopotential approximation, are used as the basis of expansion, replacing the usually very large set of plane waves in the conventional pseudopotential method. These PAO's however, do not consist of a rigorously complete set of orthonormal states.

Perceptions of a Collaborative Professional Learning Program: Seeing the “Bigger Picture”

2020 ◽  
Vol 5 (1) ◽  
pp. 290-303
Author(s):  
P. Charlie Buckley ◽  
Kimberly A. Murza ◽  
Tami Cassel
Keyword(s):  
Data Analysis ◽  
Professional Learning ◽  
Social Communication ◽  
Special Educators ◽  
Service Providers ◽  
Integrative Approach ◽  
Theory Approach ◽  
Learning Program ◽  
Speech Language Pathologists ◽  
Related Service

Purpose The purpose of this study was to explore the perceptions of special education practitioners (i.e., speech-language pathologists, special educators, para-educators, and other related service providers) on their role as communication partners after participation in the Social Communication and Engagement Triad (Buckley et al., 2015 ) yearlong professional learning program. Method A qualitative approach using interviews and purposeful sampling was used. A total of 22 participants who completed participation in either Year 1 or Year 2 of the program were interviewed. Participants were speech-language pathologists, special educators, para-educators, and other related service providers. Using a grounded theory approach (Glaser & Strauss, 1967 ) to data analysis, open, axial, and selective coding procedures were followed. Results Three themes emerged from the data analysis and included engagement as the goal, role as a communication partner, and importance of collaboration. Conclusions Findings supported the notion that educators see the value of an integrative approach to service delivery, supporting students' social communication and engagement across the school day but also recognizing the challenges they face in making this a reality.

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