Unified Rotational and Translational Stiffness Characterization of Compliant Shell Mechanisms

2018 ◽  
Author(s):  
Joost R. Leemans ◽  
Charles J. Kim ◽  
Werner W. P. J. van de Sande ◽  
Just L. Herder
Keyword(s):  
Degrees Of Freedom ◽  
Compliant Mechanisms ◽  
Screw Theory ◽  
Characterization Methods ◽  
Six Degrees Of Freedom ◽  
Thin Walled Structures ◽  
Spatial Mechanisms ◽  
Eigen Decomposition ◽  
Comprehensive Characterization

Compliant shell mechanisms utilize spatially curved thin-walled structures to transfer or transmit force, motion or energy through elastic deformation. To design with spatial mechanisms designers need comprehensive characterization methods, while existing methods fall short of meaningful comparisons between rotational and translational degrees of freedom. This paper presents two approaches, both of which are based on the principle of virtual loads and potential energy, utilizing properties of screw theory, Plücker coordinates and an eigen-decomposition, leading to two unification lengths that can be used to compare and visualize all six degrees of freedom directions and magnitudes of compliant mechanisms in a non-arbitrary physically meaningful manner.

Unified Stiffness Characterization of Nonlinear Compliant Shell Mechanisms

2018 ◽  
Vol 11 (1) ◽  
Author(s):  
Joost R. Leemans ◽  
Charles J. Kim ◽  
Werner W .P. J. van de Sande ◽  
Just L. Herder
Keyword(s):  
Degrees Of Freedom ◽  
Screw Theory ◽  
Nonlinear Behavior ◽  
Characterization Methods ◽  
Six Degrees Of Freedom ◽  
Thin Walled Structures ◽  
Nonlinear Characterization ◽  
Spatial Mechanisms ◽  
Eigen Decomposition

Compliant shell mechanisms utilize spatially curved thin-walled structures to transfer or transmit force, motion, or energy through elastic deformation. To design spatial mechanisms, designers need comprehensive nonlinear characterization methods, while the existing methods fall short of meaningful comparisons between rotational and translational degrees-of-freedom. This paper presents two approaches, both of which are based on the principle of virtual loads and potential energy, utilizing properties of screw theory, Plücker coordinates, and an eigen-decomposition. This leads to two unification lengths that can be used to compare and visualize all six degrees-of-freedom directions and magnitudes in a nonarbitrary, physically meaningful manner for mechanisms exhibiting geometrically nonlinear behavior.

Classification of Compliant Mechanisms and Determination of the Degrees of Freedom Using the Concepts of Compliance Number and Pseudo-Rigid-Body Model

2019 ◽  
Author(s):  
Pratheek Bagivalu Prasanna ◽  
Ashok Midha ◽  
Sushrut G. Bapat
Keyword(s):  
Rigid Body ◽  
Degrees Of Freedom ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Body Model ◽  
Active Compliance ◽  
Kinematic Behavior ◽  
Rigid Body Model

Abstract Understanding the kinematic properties of a compliant mechanism has always proved to be a challenge. A concept of compliance number offered earlier emphasized the development of terminology that aided in its determination. A method to evaluate the elastic degrees of freedom associated with the flexible segments/links of a compliant mechanism using the pseudo-rigid-body model (PRBM) concept is provided. In this process, two distinct classes of compliant mechanisms are developed involving: (i) Active Compliance and (ii) Passive Compliance. Furthermore, these also aid in a better characterization of the kinematic behavior of a compliant mechanism. A more lucid interpretation of the significance of compliance number is provided. Applications of this method to both active and passive compliant mechanisms are exemplified. Finally, an experimental procedure that aids in visualizing the degrees of freedom as calculated is presented.

A 2(3-RRPS) parallel manipulator inspired by Gough–Stewart platform

Robotica ◽  
2012 ◽  
Vol 31 (3) ◽  
pp. 381-388 ◽  
Author(s):  
Jaime Gallardo-Alvarado ◽  
Mario A. García-Murillo ◽  
Eduardo Castillo-Castaneda
Keyword(s):  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Screw Theory ◽  
Parallel Manipulators ◽  
Forward Kinematics ◽  
Triangular Prism ◽  
Input Output ◽  
Six Degrees Of Freedom ◽  
Moving Platform

SUMMARYThis study addresses the kinematics of a six-degrees-of-freedom parallel manipulator whose moving platform is a regular triangular prism. The moving and fixed platforms are connected to each other by means of two identical parallel manipulators. Simple forward kinematics and reduced singular regions are the main benefits offered by the proposed parallel manipulator. The Input–Output equations of velocity and acceleration are systematically obtained by resorting to reciprocal-screw theory. A case study, which is verified with the aid of commercially available software, is included with the purpose to exemplify the application of the method of kinematic analysis.

General inverse solution of six-degrees-of-freedom serial robots based on the product of exponentials model

2018 ◽  
Vol 38 (3) ◽  
pp. 361-367 ◽  
Author(s):  
Haixia Wang ◽  
Xiao Lu ◽  
Wei Cui ◽  
Zhiguo Zhang ◽  
Yuxia Li ◽  
...  
Keyword(s):  
Design Methodology ◽  
Degrees Of Freedom ◽  
Screw Theory ◽  
Complex Problem ◽  
Content Type ◽  
Geometrical Properties ◽  
Closed Form Solutions ◽  
Six Degrees Of Freedom ◽  
Serial Robots ◽  
Six Dof

Purpose Developing general closed-form solutions for six-degrees-of-freedom (DOF) serial robots is a significant challenge. This paper thus aims to present a general solution for six-DOF robots based on the product of exponentials model, which adapts to a class of robots satisfying the Pieper criterion with two parallel or intersecting axes among its first three axes. Design/methodology/approach The proposed solution can be represented as uniform expressions by using geometrical properties and a modified Paden–Kahan sub-problem, which mainly adopts the screw theory. Findings A simulation and experiments validated the correctness and effectiveness of the proposed method (general resolution for six-DOF robots based on the product of exponentials model). Originality/value The Rodrigues rotation formula is additionally used to turn the complex problem into a solvable trigonometric function and uniformly express six solutions using two formulas.

Kinematics of the Translational 3-URC Mechanism1

2004 ◽  
Vol 126 (6) ◽  
pp. 1113-1117 ◽  
Author(s):  
Raffaele Di Gregorio
Keyword(s):  
Explicit Form ◽  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Industrial Applications ◽  
Parallel Architectures ◽  
Six Degrees Of Freedom ◽  
Spatial Mechanisms ◽  
Six Dof ◽  
And Control ◽  
Spherical Motion

The use of less than six degrees of freedom (dof) mechanisms instead of six-dof ones is always recommended when the application makes it possible, since their architectures and control are simpler to manufacture and implement respectively. Three-dof mechanisms constitute an important subset of less-than-six-dof mechanisms, since either translational or spherical motion can be obtained through three-dof spatial mechanisms and many industrial applications require the only translational or spherical motion. This paper presents a new translational parallel mechanism (TPM), named translational 3-URC. The new mechanism belongs to the parallel architectures with 3-URC topology, which contain another architecture that is a spherical parallel wrist. The proposed TPM is not overconstrained and has three equal legs whose kinematic pairs are three revolute pairs and one passive cylindrical pair per leg. Its actuated pairs are three revolute pair located on the frame. The position and velocity analyses of the translational 3-URC will be addressed and solved. Its singularity conditions will be written in explicit form and geometrically interpreted.

Motion/Force Transmission Analysis of Parallel Mechanisms With Planar Closed-Loop Subchains

2016 ◽  
Vol 138 (6) ◽  
Author(s):  
Kristan Marlow ◽  
Mats Isaksson ◽  
Jian S. Dai ◽  
Saeid Nahavandi
Keyword(s):  
Performance Measures ◽  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Closed Loop ◽  
Screw Theory ◽  
Parallel Mechanisms ◽  
Force Transmission ◽  
Six Degrees Of Freedom ◽  
Lower Mobility ◽  
Transmission Ability

Singularities are one of the most important issues affecting the performance of parallel mechanisms. A parallel mechanism with less than six degrees of freedom (6DOF) is classed as having lower mobility. In addition to input–output singularities, such mechanisms potentially suffer from singularities among their constraints. Furthermore, the utilization of closed-loop subchains (CLSCs) may introduce additional singularities, which can strongly affect the motion/force transmission ability of the entire mechanism. In this paper, we propose a technique for the analysis of singularities occurring within planar CLSCs, along with a finite, dimensionless, frame invariant index, based on screw theory, for examining the closeness to these singularities. The integration of the proposed index with existing performance measures is discussed in detail and exemplified on a prototype industrial parallel mechanism.

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.

A Screw Theory-Based Semi-Analytical Approach for Elastodynamics of the Tricept Robot

2019 ◽  
Vol 11 (3) ◽  
Author(s):  
Chenglin Dong ◽  
Haitao Liu ◽  
Tian Huang ◽  
Derek G. Chetwynd
Keyword(s):  
Lower Order ◽  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Analytical Approach ◽  
Screw Theory ◽  
Mode Shapes ◽  
Fe Model ◽  
Six Degrees Of Freedom ◽  
Static Condensation ◽  
Elastodynamic Modeling

Taking the well-known Tricept robot as an example, this paper presents a semi-analytical approach for elastodynamic modeling of five or six degrees of freedom (DOF) hybrid robots composed of a 3-DOF parallel mechanism plus a 2- or 3-DOF wrist. Drawing heavily on screw theory combined with structural dynamics, the kinetic and elastic potential energies of the parallel mechanism and of the wrist are formulated using the dual properties of twist/wrench systems and a static condensation technique. This results in a 9-DOF dynamic model that enables the lower-order dynamic behavior over the entire workspace to be estimated in a very efficient and accurate manner. The lower-order natural frequencies and mode shapes estimated by the proposed approach are shown to have very good agreement with those obtained by a full-order finite element (FE) model. It thus provides a very time-effective tool for optimal design within a virtual prototyping framework for hybrid robot-based machine tools.

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.

Type synthesis of spatial mechanisms for forging manipulators

2012 ◽  
Vol 226 (9) ◽  
pp. 2320-2330 ◽  
Author(s):  
Yundou Xu ◽  
Jiantao Yao ◽  
Yongsheng Zhao
Keyword(s):  
Degrees Of Freedom ◽  
Screw Theory ◽  
Parallel Mechanisms ◽  
Type Synthesis ◽  
Heavy Duty ◽  
Systematic Method ◽  
Type Selection ◽  
Spatial Mechanisms ◽  
Selection For ◽  
Overconstrained Mechanisms

In this study, a systematic method is proposed to synthesize the parallel and hybrid serial–parallel mechanisms for the forging manipulators based on the screw theory. First, several typical configurations of five-degrees-of-freedom parallel mechanism for the forging manipulators are synthesized, and they are all non-overconstrained mechanisms. Then, two kinds of hybrid serial–parallel mechanisms for the forging manipulators with the advantages of motion decoupling are constructed, which are also not overconstrained. The configurations obtained in this study would provide more type selection for the heavy-duty forging manipulators in engineering.

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