Dimensional Synthesis of Closed-Loop Linkages to Match Force and Position Specifications

1993 ◽  
Vol 115 (2) ◽  
pp. 194-198 ◽  
Author(s):  
C. Huang ◽  
B. Roth
Keyword(s):  
Rigid Body ◽  
External Load ◽  
Closed Loop ◽  
Dimensional Synthesis ◽  
Kinematic Synthesis ◽  
Spring Element ◽  
Planar Linkages

By combining classical kinematic synthesis and static synthesis, we consider force conditions as well as motions in the dimensional synthesis of linkages. We are concerned with determining the dimensions of linkages that guide a rigid body through several positions and support a specified external load at each position. Three types of planar linkages are studied in detail: four-bar, slider-crank, and double-slider linkages. Incompletely specified problems and spring element synthesis are also discussed.

Kinematic Synthesis of Minimally Actuated Multi-Loop Planar Linkages With Second Order Motion Constraints for Object Grasping

2013 ◽  
Author(s):  
Gim Song Soh ◽  
Nina Robson
Keyword(s):  
Second Order ◽  
Human Robot Interaction ◽  
Degree Of Freedom ◽  
Dimensional Synthesis ◽  
Open Problems ◽  
Kinematic Synthesis ◽  
Human Environment ◽  
Kinematic Chains ◽  
Curvature Effects ◽  
Planar Linkages

In this paper, we consider the dimensional synthesis of one degree-of-freedom multi-loop planar linkages such that they do not violate normal direction and second order curvature constraints imposed by contact with objects. Our goal is in developing minimally actuated multi-loop mechanical devices for human-robot interaction, that is, devices whose tasks will happen in a human environment. Currently no systematic method exists for the kinematic synthesis of robotic fingers that incorporate multi-loop kinematic structure with second order task constraints, related to curvature. We show how to use these contact and curvature effects to formulate the synthesis equations for the design of a planar one-degree-of-freedom six-bar linkage. An example for the design of a finger that maintains a specified contact with an object, for an anthropomorphic task, is presented at the end of the paper. It is important to note, that the theoretical foundation presented in this paper, assists in solving some of the open problems of this field, providing preliminary results on the synthesis of kinematic chains with multi-loop topology and the use of novel task specifications that incorporate curvature constraints with future applications in grasping and object manipulation.

Geometric design of planar mechanisms based on virtual guides for manipulation

Robotica ◽  
2015 ◽  
Vol 34 (12) ◽  
pp. 2653-2668 ◽  
Author(s):  
Nina Robson ◽  
Shramana Ghosh
Keyword(s):  
Rigid Body ◽  
Closed Loop ◽  
Normal Direction ◽  
Assistive Technologies ◽  
Paper Briefly ◽  
Planar Mechanisms ◽  
Kinematic Synthesis ◽  
Kinematic Chains ◽  
Moving Body ◽  
Mechanical Linkage

SUMMARYThis paper presents recent results and applications of our planar kinematic synthesis of serial and parallel linkages to guide a rigid body, such that it does not violate normal direction and curvature constraints imposed by contact with objects in the environment. The paper briefly reviews the recently developed theory on transforming contact direction and curvature constraints into conditions on velocity and acceleration of certain points in the moving body to obtain synthesis equations which can, subsequently be solved to find the dimensions of a mechanical linkage. The main contribution of the paper is in demonstrating the applicability of the proposed theory to the kinematic synthesis of both open and closed-loop kinematic linkages. We provide preliminary results on the synthesis of kinematic chains based on novel task specifications that incorporate curvature constraints with a variety of applications, such as passive suspensions for small rovers, assistive technologies, as well as grasping.

Geometric Design of Symmetric 3-RRS Constrained Parallel Platforms

2004 ◽  
Author(s):  
Eric Wolbrecht ◽  
Hai-Jun Su ◽  
Alba Perez ◽  
J. Michael McCarthy
Keyword(s):  
Geometric Design ◽  
Homotopy Continuation ◽  
Total Degree ◽  
Polynomial Equations ◽  
Dimensional Synthesis ◽  
Kinematic Synthesis ◽  
Real Solutions ◽  
Parallel Platform ◽  
Three Degree Of Freedom ◽  
Serial Chains

The paper presents the kinematic synthesis of a symmetric parallel platform supported by three RRS serial chains. The dimensional synthesis of this three degree-of-freedom system is obtained using design equations for each of three RRS chains obtained by requiring that they reach a specified set of task positions. The result is 10 polynomial equations in 10 unknowns, which is solved using polynomial homotopy continuation. An example is provided in which the direction of the first revolute joint (2 parameters) and the z component of the base and platform are specified as well as the two task positions. The system of polynomials has a total degree of 4096 which means that in theory it can have as many solutions. Our example has 70 real solutions that define 70 different symmetric platforms that can reach the specified positions.

scholarly journals Kinematic synthesis of planar, shape-changing, rigid body mechanisms for design profiles with significant differences in arc length

2013 ◽  
Vol 70 ◽  
pp. 425-440 ◽  
Author(s):  
Shamsul A. Shamsudin ◽  
Andrew P. Murray ◽  
David H. Myszka ◽  
James P. Schmiedeler
Keyword(s):  
Rigid Body ◽  
Arc Length ◽  
Kinematic Synthesis ◽  
Planar Shape

Kinematic Synthesis of a D-Drive MEMS Device With Rigid-Body Replacement Method

2018 ◽  
Vol 140 (7) ◽  
Author(s):  
Paolo Sanò ◽  
Matteo Verotti ◽  
Paolo Bosetti ◽  
Nicola P. Belfiore
Keyword(s):  
Rigid Body ◽  
Experimental Testing ◽  
Micro Electro Mechanical System ◽  
Element Analysis ◽  
Kinematic Synthesis ◽  
Replacement Method ◽  
Rigid Body Model ◽  
Mems Device ◽  
Conjugate Surfaces ◽  
Line Path

In this paper, a microsystem with prescribed functional capabilities is designed and simulated. In particular, the development of a straight line path generator micro electro mechanical system (MEMS) device is presented. A new procedure is suggested for avoiding branch or circuit problems in the kinematic synthesis problem. Then, Ball's point detection is used to validate the obtained pseudo-rigid body model (PRBM). A compliant MEMS device is obtained from the PRBM through the rigid-body replacement method by making use of conjugate surfaces flexure hinges (CSFHs). Finally, the functional capability of the device is investigated by means of finite element analysis (FEA) simulations and experimental testing at the macroscale.

Designing Planar Mechanisms Using a Bi-Invariant Metric in the Image Space of SO (3)

1994 ◽  
Author(s):  
Pierre Larochelle ◽  
J. Michael McCarthy
Keyword(s):  
Rigid Body ◽  
Numerical Results ◽  
Image Space ◽  
Dimensional Synthesis ◽  
Invariant Metric ◽  
Planar Mechanisms ◽  
Position And Orientation ◽  
Position Synthesis

Abstract In this paper we present a technique for using a bi-invariant metric in the image space of spherical displacements for designing planar mechanisms for n (> 5) position rigid body guidance. The goal is to perform the dimensional synthesis of the mechanism such that the distance between the position and orientation of the guided body to each of the n goal positions is minimized. Rather than measure these distances in the plane, we introduce an approximating sphere and identify rotations which are equivalent to the planar displacements to a specified tolerance. We then measure distances between the rigid body and the goal positions using a bi-invariant metric on the image space of SO(3). The optimal linkage is obtained by minimizing this distance over all of the n goal positions. The paper proceeds as follows. First, we approximate planar rigid body displacements with spherical displacements and show that the error induced by such an approximation is of order 1/R2, where R is the radius of the approximating sphere. Second, we use a bi-invariant metric in the image space of spherical displacements to synthesize an optimal spherical 4R mechanism. Finally, we identify the planar 4R mechanism associated with the optimal spherical solution. The result is a planar 4R mechanism that has been optimized for n position rigid body guidance using an approximate bi-invariant metric with an error dependent only upon the radius of the approximating sphere. Numerical results for ten position synthesis of a planar 4R mechanism are presented.

Kinematic Synthesis of Spatial R-R Dyads for Path Following Revisited Using the Rotation Matrix Approach

1999 ◽  
Author(s):  
Venkat Krovi ◽  
G. K. Ananthasuresh ◽  
Vijay Kumar
Keyword(s):  
Linear System ◽  
Path Following ◽  
Rotation Matrix ◽  
Dimensional Synthesis ◽  
Kinematic Synthesis ◽  
End Effector ◽  
Serial Chain ◽  
Systematic Development ◽  
Matrix Vector ◽  
Selection Of

Abstract We revisit the dimensional synthesis of a spatial two-link, two revolute-jointed serial chain for path following applications, focussing on the systematic development of the design equations and their analytic solution for the three precision point synthesis problem. The kinematic design equations are obtained from the equations of loop-closure for end-effector position in rotation-matrix/vector form at the three precision points. These design equations form a rank-deficient linear system in the link-vector components. The nullspace of the rank deficient linear system is then deduced analytically and interpreted geometrically. Tools from linear algebra are applied to systematically create the auxiliary conditions required for synthesis and to verify consistency. An analytic procedure for obtaining the link-vector components is then developed after a suitable selection of free choices. Optimization over the free choices is possible to permit the matching of additional criteria and explored further. Examples of the design of optimal two-link coupled spatial R-R dyads are presented where the end-effector interpolates three positions exactly and closely approximates an entire desired path.

scholarly journals Formulation and Simulations of the Conserving Algorithm for Feedback Stabilization on Rigid Body Rotations

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Yong-Ren Pu ◽  
Thomas A. Posbergh
Keyword(s):  
Rigid Body ◽  
Closed Loop ◽  
Numerical Algorithms ◽  
Open Loop ◽  
Rigid Bodies ◽  
Feedback Stabilization ◽  
Conserved Quantities ◽  
Control Laws ◽  
Loop Control ◽  
Closed Loop Systems

The problem of stabilization of rigid bodies has received a great deal of attention for many years. People have developed a variety of feedback control laws to meet their design requirements and have formulated various but mostly open loop numerical algorithms for the dynamics of the corresponding closed loop systems. Since the conserved quantities such as energy, momentum, and symmetry play an important role in the dynamics, we investigate the conserved quantities for the closed loop control systems which formally or asymptotically stabilize rigid body rotation and modify the open loop numerical algorithms so that they preserve these important properties. Using several examples, the authors first use the open loop algorithm to simulate the tumbling rigid body actions and then use the resulting closed loop one to stabilize them.

Finding All Solutions to Unconstrained Nonlinear Optimization for Approximate Synthesis of Planar Linkages Using Continuation Method

1999 ◽  
Vol 121 (3) ◽  
pp. 368-374 ◽  
Author(s):  
A.-X. Liu ◽  
T.-L. Yang
Keyword(s):  
Continuation Method ◽  
Optimization Method ◽  
Global Optimum ◽  
Kinematic Synthesis ◽  
All Solutions ◽  
Approximate Synthesis ◽  
Unconstrained Nonlinear Optimization ◽  
Optimum Solution ◽  
Planar Linkages ◽  
Four Bar Linkage

Generally, approximate kinematic synthesis of planar linkage is studied using optimization method. But this method has two defects: i) the suitable initial guesses are hard to determine and ii) the global optimum solution is difficult to find. In this paper, a new method which can find all solutions to approximate kinematic synthesis of planar linkage is proposed. Firstly, we reduce the approximate synthesis problem to finding all solutions to polynomial equations. Polynomial continuation method is then used to find all solutions. Finally, all possible linkages can be obtained. Approximate syntheses of planar four-bar linkage for function generation, rigid-body guidance and path generation are studied in detail and three examples are given to illustrate the advantages of the proposed method.

Singularity Analysis of Rigid-Body, Closed-Loop, Shape-Changing Mechanisms

2008 ◽  
Author(s):  
David Myszka ◽  
Andrew Murray ◽  
James Schmiedeler
Keyword(s):  
Rigid Body ◽  
Body Shape ◽  
Closed Loop ◽  
Singularity Analysis ◽  
Closed Contour ◽  
Condensed Form ◽  
Loop Shape

This paper presents an analysis to create a general singularity condition for a mechanism that contains a deformable closed contour. This kinematic architecture is widely used in rigid-body shape changing mechanisms. The general singularity equation is reduced to a condensed form, which allows geometric relationships to be readily detected. A method for formulating the singularity condition for a mechanism with N links in the closed contour, knowing the condition for the N − 1 mechanism, is also given.

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