Software for the Kinematic Synthesis of Coupler-Driven Spherical Four-Bar Mechanisms

2007 ◽  
Author(s):  
Eric M. Grimm ◽  
Andrew P. Murray ◽  
Michael L. Turner
Keyword(s):  
Rigid Body ◽  
Kinematic Synthesis ◽  
Prismatic Joint ◽  
Second Stage ◽  
Typical Scheme ◽  
Four Bar Linkage

A spatial analogue of the Stephenson III six-bar mechanism can be formed by the connection of an SPS chain to the coupler of a spherical four-bar linkage. With the prismatic joint actuated, the spherical four-bar is driven via a force applied directly to the coupler. This linkage is termed the coupler-driven spherical four-bar mechanism, and defines an alternative to the typical scheme of actuating the four-bar via a torque applied at the input link. This paper presents software developed to assist in the kinematic synthesis of these mechanisms. In the first stage of the design, a circuit-defect free spherical four-bar is dimensioned with the capacity to guide a rigid body through two orientations. The second stage of the design is to locate the SPS leg such that the four-bar is smoothly drivable between the orientations.

The Kinematic Synthesis of a Robust RCCC Mechanism for Pick-and-Place Operations

2012 ◽  
Author(s):  
Khalid M. Al-Widyan ◽  
Jorge Angeles
Keyword(s):  
Rigid Body ◽  
Robust Design ◽  
Theoretical Framework ◽  
Synthesis Problem ◽  
Kinematic Synthesis ◽  
General Methodology ◽  
Pick And Place ◽  
Four Bar Linkage ◽  
Pick And Place Operation ◽  
Selection Of

Proposed in this paper is a methodology to synthesize a RCCC four-bar linkage intended for pick-and-place operations. The synthesis problem is set in the context of rigid-body guidance, which can be solved exactly for up to four prescribed poses of the coupler link. As a consequence, for a pick-and-place operation, the selection of the unspecified two intermediate poses is thus left up to the mechanism designer’s judgment. In this paper, we propose a method to determine the two intermediate poses resorting to the concept of robustness. In fact, robustness is needed in this context to overcome the presence of uncertainty due to the selection of the two unspecified poses. To this end, a theoretical framework for model-based robust design is invoked and a general methodology for robust kinematic synthesis is laid down. A numerical example is included to validate the concepts and illustrate the application of the methodology proposed here.

Kinematic Synthesis of Binary Actuated Mechanisms for Rigid Body Guidance

2000 ◽  
Author(s):  
Michael S. Hanchak ◽  
Andrew P. Murray
Keyword(s):  
Rigid Body ◽  
Design Space ◽  
Kinematic Synthesis ◽  
Prismatic Joint ◽  
Revolute Joints ◽  
Binary State ◽  
Parallel Arrangement ◽  
Position Problem ◽  
Position Synthesis ◽  
Kinematic Solution

Abstract This paper presents a method for designing mechanisms composed of Revolute-Binary state prismatic-Revolute (RBR) chains for rigid body guidance. Where a prismatic joint allows for any distance between two revolute joints, a binary state prismatic joint reaches two distances precisely. A single RBR chain can be designed to reach six positions. A parallel arrangement of three RBR chains can be assembled at the six positions but, in general, is not a viable kinematic solution. By requiring the arrangement of three RBR chains to share specific fixed and moving pivots, called an N-type arrangement, four positions are reachable. Further, the design space is quickly searchable for singularity-free solutions. Examples illustrate a solution to a four position synthesis problem and a ten position problem using a serial assembly of these mechanisms.

The Robust Linkage Synthesis for Planar Rigid-Body Guidance

2010 ◽  
Author(s):  
Khalid Al-Widyan ◽  
Jorge Angeles
Keyword(s):  
Rigid Body ◽  
Robust Design ◽  
Theoretical Framework ◽  
Planar Motion ◽  
Kinematic Synthesis ◽  
The Subject ◽  
Four Bar Linkage ◽  
Guidance Problem ◽  
Selection Of ◽  
Linkage Synthesis

The kinematic synthesis of planar motion generators in the presence of an incomplete set of finitely separated poses is the subject of this paper. Given that the planar rigid-body guidance problem in the realm of four-bar linkage synthesis can be solved exactly for up to five prescribed poses of the coupler link, any number of poses smaller than five is considered incomplete in this paper. The poses completing the set are determined so as to produce a robust linkage against variations in the unspecified poses. To this end, a theoretical framework for model-based robust design is invoked and a general methodology for robust kinematic synthesis is laid down. Robustness is needed in this context to overcome the presence of uncertainty due to the selection of the unprescribed poses, which many a time are left up to the mechanism designer’s judgment. To validate the concepts and illustrate the application of the methodology proposed here, an example is included.

On the Seven Position Synthesis of a 5-SS Platform Linkage

1997 ◽  
Vol 123 (1) ◽  
pp. 74-79 ◽  
Author(s):  
Qizheng Liao ◽  
J. Michael McCarthy
Keyword(s):  
Rigid Body ◽  
Reference Point ◽  
Polynomial Solution ◽  
Degree Of Freedom ◽  
Prismatic Joint ◽  
Movement Characteristics ◽  
Position Synthesis ◽  
Freedom Movement

This paper builds on Innocenti’s polynomial solution for the 5-SS platform that generates a one-degree of freedom movement through seven specified spatial positions of a rigid body. We show that his 60×60 resultant can be reduced to one that is 10×10. We then actuate the linkage using a prismatic joint on the sixth leg and determine the trajectory of the reference point through the specified positions. The singularity submanifold of this associated 6-SS platform provides information about the movement characteristics of the 5-SS linkage.

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.

THE KINEMATIC SYNTHESIS OF STEERING MECHANISMS

2000 ◽  
Vol 24 (3-4) ◽  
pp. 453-476 ◽  
Author(s):  
Jin Yao ◽  
Jorge Angeles
Keyword(s):  
Polynomial Equation ◽  
Global Optimum ◽  
Polynomial Equations ◽  
Kinematic Synthesis ◽  
Local Optima ◽  
Speed Reduction ◽  
Design Variables ◽  
Transmission Quality ◽  
Four Bar Linkage ◽  
Maximum Transmission

We propose a computational-kinematics approach based on elimination procedures to synthesize a steering four-bar linkage. In this regard, we aim at minimizing the root-mean square error of the synthesized linkage in meeting the steering condition over a number of linkage configurations within the linkage range of motion. A minimization problem is thus formulated, whose normality conditions lead to two polynomial equations in two unknown design variables. Upon eliminating one of these two variables, a monovariate polynomial equation is obtained, whose roots yield all locally-optimum linkages. From these roots, the global optimum, as well as unfeasible local optima, are readily identified. The global optimum, however, turns out to be impractical because of the large differences in its link lengths, which we refer to as dimensional unbalance. To cope with this drawback, we use a kinematically-equivalent focal mechanism, i.e., a six-bar linkage with an input-output function identical to that of the four-bar linkage. Given that the synthesized linkage requires a rotational input, as opposed to most existing steering linkages, which require a translational input, we propose a spherical four-bar linkage to drive the steering linkage. The spherical linkage is synthesized so as to yield a speed reduction as close as possible to 2:1 and to have a maximum transmission quality.

A frame-independent comparison metric for discrete motion sequences

2020 ◽  
Vol 234 (9) ◽  
pp. 1764-1774
Author(s):  
Ping Zhao ◽  
Yong Wang ◽  
Lihong Zhu ◽  
Xiangyun Li
Keyword(s):  
Moving Frame ◽  
Kinematic Synthesis ◽  
Reference Motion ◽  
Comparison Results ◽  
Synthesis Of Mechanisms ◽  
Rotational Part ◽  
The Difference ◽  
Four Bar Linkage ◽  
The Given ◽  
Discrete Motion

To evaluate the kinematic performance of designed mechanisms, a statistical-variance-based metric is proposed in this article to measure the “distance” between two discrete motion sequences: the reference motion and the given task motion. It seeks to establish a metric that is independent of the choice of the fixed frame or moving frame. Quaternions are adopted to represent the rotational part of a spatial pose, and the variance of the set of relative displacements is computed to reflect the difference between two sequences. With this variance-based metric formulation, we show that the comparison results of two spatial discrete motions are not affected by the choice of frames. Both theoretical demonstration and computational example are presented to support this conclusion. In addition, since the deviation error between the task motion and the synthesized motion measured with this metric is independent of the location of frames, those corresponding parameters could be excluded from the optimization algorithm formulated with our frame-independent metric in kinematic synthesis of mechanisms, and the complexity of the algorithm are hereby reduced. An application of a four-bar linkage synthesis problem is presented to illustrate the advantage of the proposed metric.

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.

Synthesis of Six-Bar Timed Curve Generators of Stephenson-Type Using Random Monodromy Loops

2020 ◽  
Vol 13 (1) ◽  
Author(s):  
Aravind Baskar ◽  
Mark Plecnik
Keyword(s):  
Rigid Body ◽  
Complete Solution ◽  
Numerical Algebraic Geometry ◽  
Algebraic Equations ◽  
Solution Sets ◽  
Root Finding ◽  
Rigid Body Motions ◽  
Joint Variable ◽  
Four Bar Linkage ◽  
Parameter Continuation

Abstract Synthesis of rigid-body mechanisms has traditionally been motivated by the design for kinematic requirements such as rigid-body motions, paths, or functions. A blend of the latter two leads to timed curve synthesis, the goal of which is to produce a path coordinated to the input of a joint variable. This approach has utility for altering the transmission of forces and velocities from an input joint onto an output point path. The design of timed curve generators can be accomplished by setting up a square system of algebraic equations and obtaining all isolated solutions. For a four-bar linkage, obtaining these solutions is routine. The situation becomes much more complicated for the six-bar linkages, but the range of possible output motions is more diverse. The computation of nearly complete solution sets for these six-bar design equations has been facilitated by recent root finding techniques belonging to the field of numerical algebraic geometry. In particular, we implement a method that uses random monodromy loops. In this work, we report these solution sets to all relevant six-bars of the Stephenson topology. The computed solution sets to these generic problems represent a design library, which can be used in a parameter continuation step to design linkages for different subsequent requirements.

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