0
RESEARCH PAPERS

Automatic Synthesis of a Planar Linkage Mechanism With Revolute Joints by Using Spring-Connected Rigid Block Models

[+] Author and Article Information
Yoon Young Kim

School of Mechanical and Aerospace Engineering and National Creative Research Initiatives Center for Multiscale Design, Seoul National University, Seoul 151-742, Koreayykim@snu.ac.kr

Gang-Won Jang

School of Mechanical Engineering, Kunsan National University, Kunsan, Chonbuk 573-701, Korea

Jung Hun Park

 Brooks Automation Asia, Gomaeri 398-1, Kiheung, Yongin, Kyungki 449-901, Korea

Jin Sub Hyun, Sang Jun Nam

School of Mechanical and Aerospace Engineering and National Creative Research Initiative Center for Multiscale Design, Seoul National University, Seoul 151-742, Korea

Some preliminary results of the automatic synthesis method were presented as the plenary lecture at the 3rd China-Japan-Korea Joint Symposium on Optimization of Structural and Mechanical Systems (Kanazawa, Japan, Oct. 30–Nov. 2, 2004). They were also presented in topoptSYMP2005 (Copenhagen, Denmark, Oct. 31–Nov. 3, 2005).

Although the developed Strategy III is expected to handle the mechanism synthesis involving dynamics, we limit our attention to statics in this investigation.

The symbol kp,α refers to either a spring or its stiffness to avoid too many symbols.

Readers interested in the ADAMS input files used to solve all case studies may contact the corresponding author.

J. Mech. Des 129(9), 930-940 (Sep 12, 2006) (11 pages) doi:10.1115/1.2747636 History: Received November 28, 2005; Revised September 12, 2006

In traditional linkage design practice, a designer first decides the specific linkage type, such as a four- or six-bar linkage, and then varies the joint locations and link lengths until the designer finds the desired linkage. The objective of this research is to establish an automatic mechanism synthesis method that determines the linkage type and dimensions during the synthesis process. The synthesis process can be formulated as a minimization problem. However, the process can be extremely difficult and time-consuming unless there is a single unified linkage model that represents any linkage mechanism without complicating kinematic analysis and allows the use of an efficient gradient-based optimizer. The main contribution of this investigation is to propose a unified planar linkage model consisting of rigid blocks connected by zero-length springs having real-valued variable stiffness. Stiffness controlling variables are the design variable of the minimization problem and a general planar linkage can be simulated by the spring-connected rigid block model if the stiffness value is chosen appropriately. Though mechanisms involving only revolute joints are investigated and the solved problems are relatively simple, the notion of the block model and the synthesis formulation in real variables are expected to give a different perspective on mechanism synthesis.

Copyright © 2007 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Figure 1

Problem definition: for given input and output motions, find a planar linkage mechanism without relying on any baseline linkage

Grahic Jump Location
Figure 2

Spring-connected block model: (a) discretization of a mechanism configuration domain by a number of rigid rectangular blocks and (b) a set of zero-length elastic springs with variable stiffness connecting adjacent rigid blocks

Grahic Jump Location
Figure 3

Discretized linkage model consisting of short links and (connectors): (a) discretization of the mechanism configuration domain and (b) a four-bar linkage representation

Grahic Jump Location
Figure 4

Planar linkage modeling by Strategy II: (a) link connection by a set of translational and rotational springs and (b) modeling verification (k12T=kmaxT, k12R=kminR; k23T=kmaxT, k23R=kmaxR; k34T=kmaxT, k34R=kmaxR; k45T=kmaxT, k45R=kminR; k56T=kmaxT, k56R=kmaxR)

Grahic Jump Location
Figure 5

Application of a spring-connected block model (SBM) for planar linkage motion simulation: (a) various connector conditions simulated by spring stiffness adjustment and (b) simple motion simulation by SBM

Grahic Jump Location
Figure 6

The use of the generalized spring-connected rigid block model (G-SBM) to represent JA in addition to D, J, and R: (a) illustration of G-SBM equivalent to a given model (Model G), (b) modeling of a rigid link having an anchored revolute joint at Q by G-SBM, and (c) motion simulation by G-SBM of (b)

Grahic Jump Location
Figure 7

Four-bar linkage design problem: (a) a target mechanism and (b) a discretized mechanism configuration domain

Grahic Jump Location
Figure 8

Iteration history of the automatic mechanism synthesis by using SBM

Grahic Jump Location
Figure 9

Linkage mechanism identification: (a) the motion of the converged SBM at t=tf and (b) the identified four-bar linkage

Grahic Jump Location
Figure 10

(a) The distribution of the converged spring stiffnesses for the problem shown in Fig. 7 and (b) the S-shaped function in Eq. 7(t=0.1)

Grahic Jump Location
Figure 11

Initial and final results of the shape optimization for the linkage in Fig. 9 (solid link: target link, void link: optimized link)

Grahic Jump Location
Figure 12

Mechanism configuration domain for the synthesis of a straight line mechanism

Grahic Jump Location
Figure 13

Iteration history of the SBM method for the straight line mechanism

Grahic Jump Location
Figure 14

Linkage mechanism identification

Grahic Jump Location
Figure 15

The locus of the end-effector after shape optimization for the straight line mechanism

Grahic Jump Location
Figure 16

Synthesis of an open-link mechanism by G-SBM: (a) a target mechanism and (b) the motion of the converged G-SBM at t=tf and its identified link mechanism

Grahic Jump Location
Figure 17

Iteration history of the open-link problem

Grahic Jump Location
Figure 18

Synthesis of a closed-link mechanism having an anchored joint: (a) a target mechanism and (b) the motion of the converged SBM at t=tf and its identified link mechanism

Grahic Jump Location
Figure 19

Iteration history of the closed-link problem by using G-SBM

Grahic Jump Location
Figure 20

Application of G-SBM for the synthesis of a vertical-line mechanism: (a) a discretized synthesis domain and (b) the motion of the converged G-SBM at t=tf and the identified link mechanism

Grahic Jump Location
Figure 21

Motion history of the synthesized link mechanism before and after shape optimization

Grahic Jump Location
Figure 22

The loci of the end-effector after shape optimization

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In