Synthesis of Planar Compliances With Mechanisms Having Six Compliant Components: Geometric Approach

2020 ◽  
Vol 12 (3) ◽  
Author(s):  
Shuguang Huang ◽  
Joseph M. Schimmels
Keyword(s):  
Compliant Mechanism ◽  
Geometric Approach ◽  
Geometric Construction ◽  
Elastic Component ◽  
Parallel Mechanisms ◽  
Elastic Joints

Abstract In this paper, the synthesis of any planar compliance with a six-component compliant mechanism is addressed. The mechanisms studied are either serial mechanisms with six elastic joints or parallel mechanisms with six springs. For each type of mechanism, conditions on the mechanism configurations that must be satisfied to realize a given compliance are developed. The geometric significance of each condition is identified and graphically represented. Geometric construction-based synthesis procedures for both types of mechanism are developed. These procedures allow one to select each elastic component from a restricted space based on its geometry.

scholarly journals Geometric Approach to the Realization of Planar Elastic Behaviors With Mechanisms Having Four Elastic Components

2018 ◽  
Vol 10 (4) ◽  
Author(s):  
Shuguang Huang ◽  
Joseph M. Schimmels
Keyword(s):  
Sufficient Conditions ◽  
Geometric Approach ◽  
Necessary And Sufficient Conditions ◽  
Elastic Component ◽  
Elastic Behavior ◽  
Parallel Mechanisms ◽  
Compliant Joints ◽  
Necessary And Sufficient ◽  
Selection Of

This paper addresses the passive realization of any selected planar elastic behavior with redundant elastic manipulators. The class of manipulators considered are either serial mechanisms having four compliant joints or parallel mechanisms having four springs. Sets of necessary and sufficient conditions for mechanisms in this class to passively realize an elastic behavior are presented. The conditions are interpreted in terms of mechanism geometry. Similar conditions for nonredundant cases are highly restrictive. Redundancy yields a significantly larger space of realizable elastic behaviors. Construction-based synthesis procedures for planar elastic behaviors are also developed. In each, the selection of the mechanism geometry and the selection of joint/spring stiffnesses are completely decoupled. The procedures require that the geometry of each elastic component be selected from a restricted space of acceptable candidates.

Determination of Maximal Singularity-Free Workspace of Parallel Mechanisms Using Constructive Geometric Approach

2013 ◽  
pp. 307-314
Author(s):  
Mohammad Hadi Farzaneh Kaloorazi ◽  
Mehdi Tale Masouleh ◽  
Stéphane Caro ◽  
Behnam Mashhadi Gholamali
Keyword(s):  
Geometric Approach ◽  
Parallel Mechanisms ◽  
Maximal Singularity

GEOMETRIC ANALYSIS OF THE KINEMATIC SENSITIVITY OF PLANAR PARALLEL MECHANISMS

2011 ◽  
Vol 35 (4) ◽  
pp. 477-490 ◽  
Author(s):  
Mohammad Hossein Saadatzi ◽  
Mehdi Tale Masouleh ◽  
Hamid D. Taghirad ◽  
Clément Gosselin ◽  
Philippe Cardou
Keyword(s):  
Physical Meaning ◽  
Performance Index ◽  
Geometric Analysis ◽  
Geometric Approach ◽  
Sensitivity Index ◽  
Parallel Mechanisms ◽  
Dimensional Synthesis ◽  
Kinematic Sensitivity

The kinematic sensitivity is a unit-consistent measure that has been recently proposed as a mechanism performance index to compare robot architectures. This paper presents a robust geometric approach for computing this index for the case of planar parallel mechanisms. The physical meaning of the kinematic sensitivity is investigated through different combinations of the Euclidean and infinity norms and by means of several illustrative examples. Finally, this paper opens some avenues to the dimensional synthesis of parallel mechanisms by exploring the meaning of the global kinematic sensitivity index.

scholarly journals On the Geometric Approach to the Boundary Problem in Supergravity

Universe ◽  
2021 ◽  
Vol 7 (12) ◽  
pp. 463
Author(s):  
Laura Andrianopoli ◽  
Lucrezia Ravera
Keyword(s):  
Cosmological Constant ◽  
Boundary Problem ◽  
Geometric Approach ◽  
Geometric Construction ◽  
Boundary Values ◽  
Negative Cosmological Constant ◽  
Boundary Terms ◽  
Bonnet Term ◽  
Topological Boundary ◽  
Field Strengths

We review the geometric superspace approach to the boundary problem in supergravity, retracing the geometric construction of four-dimensional supergravity Lagrangians in the presence of a non-trivial boundary of spacetime. We first focus on pure N=1 and N=2 theories with negative cosmological constant. Here, the supersymmetry invariance of the action requires the addition of topological (boundary) contributions which generalize at the supersymmetric level the Euler-Gauss-Bonnet term. Moreover, one finds that the boundary values of the super field-strengths are dynamically fixed to constant values, corresponding to the vanishing of the OSp(N|4)-covariant supercurvatures at the boundary. We then consider the case of vanishing cosmological constant where, in the presence of a non-trivial boundary, the inclusion of boundary terms involving additional fields, which behave as auxiliary fields for the bulk theory, allows to restore supersymmetry. In all the cases listed above, the full, supersymmetric Lagrangian can be recast in a MacDowell-Mansouri(-like) form. We then report on the application of the results to specific problems regarding cases where the boundary is located asymptotically, relevant for a holographic analysis.

scholarly journals Geometric Construction-Based Realization of Planar Elastic Behaviors With Parallel and Serial Manipulators

2017 ◽  
Vol 9 (5) ◽  
Author(s):  
Shuguang Huang ◽  
Joseph M. Schimmels
Keyword(s):  
Elastic Properties ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Geometric Construction ◽  
Elastic Component ◽  
Elastic Behavior ◽  
Serial Manipulators ◽  
New Construction ◽  
Necessary And Sufficient ◽  
Serial Mechanism

This paper addresses the passive realization of any selected planar elastic behavior with a parallel or a serial manipulator. Sets of necessary and sufficient conditions for a mechanism to passively realize an elastic behavior are presented. These conditions completely decouple the requirements on component elastic properties from the requirements on mechanism kinematics. The restrictions on the set of elastic behaviors that can be realized with a mechanism are described in terms of acceptable locations of realizable elastic behavior centers. Parallel–serial mechanism pairs that realize identical elastic behaviors (dual elastic mechanisms) are described. New construction-based synthesis procedures for planar elastic behaviors are developed. Using these procedures, one can select the geometry of each elastic component from a restricted space of kinematically allowable candidates. With each selection, the space is further restricted until the desired elastic behavior is achieved.

A Geometric Constructive Approach for the Workspace Analysis of Symmetrical 5-PRUR Parallel Mechanisms (3T2R)

2010 ◽  
Author(s):  
Mehdi Tale Masouleh ◽  
Mohammad Hossein Saadatzi ◽  
Cle´ment Gosselin ◽  
Hamid D. Taghirad
Keyword(s):  
Geometric Approach ◽  
General Mechanism ◽  
Parallel Mechanisms ◽  
Type Synthesis ◽  
End Effector ◽  
Workspace Analysis ◽  
Architecture Optimization ◽  
Insight Into ◽  
Orientation Workspace

This paper investigates an important kinematic property, the constant-orientation workspace, of five-degree-of-freedom parallel mechanisms generating the 3T2R motion and comprising five identical limbs of the PRUR type. The general mechanism originates from the type synthesis performed for symmetrical 5-DOF parallel mechanism. In this study, the emphasis is placed on the determination of constant-orientation workspace using geometrical interpretation of the so-called vertex space, i.e., motion generated by a limb for a given orientation, rather than relying on classical recipes, such as discretization methods. For the sake of better understanding a CAD model is also provided for the vertex space. The constructive geometric approach presented in this paper provides some insight into the architecture optimization. Moreover, this approach facilitates the computation of the evolution of the volume of the constant-orientation workspace for different orientations of the end-effector.

The Research on the Redundant Actuated Parallel Robot With Full Compliant Mechanism

2007 ◽  
Author(s):  
Guangping He ◽  
Zhen Lu
Keyword(s):  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Parallel Robot ◽  
Main Task ◽  
Parallel Mechanisms ◽  
Modeling And Control ◽  
Optical Instruments ◽  
Working Space ◽  
And Control ◽  
Small Working

In the field of MEMS, optical instruments and communication, the manipulation tasks such as mechanics property test of micro-material, micro-components assembling, and fibers connecting, are challenging for their minuteness and accuracy. It is measured in the scale of micrometer or sub micrometer. The full-compliant mechanisms are the best alternative, which are characteristically of their compliant hinge, and monolithic chip forming, and can be used for transmit a certain high-accuracy motion. Nevertheless, the full-compliant mechanisms have some shortages, for instance, small working space, nonlinear in large range motion, complicated in kinematical and mechanics etc. inherited from the parallel mechanisms that instructs the design of full-compliant mechanism generally. In this article, the redundant actuated parallel robot with full compliant is introduced to overcome some shortcomings of the full-compliant mechanism. The redundant actuated mechanisms provide redundant inputs and can be used in some complicated force manipulations, for example, improving the stress distribution while implements the main task for enhancing the fatigue nature of the complaint mechanism itself. As an example, a 3-DOF planar redundant actuated full-complaint robot is studied both in the modeling and control system.

A Geometric Approach to the Conic Sections

1966 ◽  
Vol 59 (4) ◽  
pp. 348-350
Author(s):  
Maurice Marie Byrne
Keyword(s):  
Geometric Approach ◽  
Geometric Construction ◽  
Conic Sections ◽  
Algebra Ii ◽  
Definition Of

Connie Byron, a student in an Algebra II class,* attempted a demonstration of how the locus of points fulfills the definition of a hyperbola by a geometric construction, based on the use of a circle as representing the constant difference. Although not conclusive in determining the locus at the time, this method was the stimulus for further study and investigation of a unique geometric approach to each of the conic sections.

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