Four-bar motion generation with elasticity constraints and optimization

Y. M. Al-Smadi, K. Russell, R. S. Sodhi

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


In conventional planar four-bar motion generation, all mechanism links are assumed rigid or non-deforming. Although the assumption of link rigidity in kinematic synthesis may be generally appropriate and often practiced, a statically loaded planar four-bar mechanism will undergo a degree of elastic deflection, particularly the crank and follower links. In this work, a non-linear optimization problem is formulated for planar four-bar motion generation that considers an applied coupler force and corresponding crank static torque, crank transverse deflection, and follower buckling. The output from the non-linear optimization problem - mechanism fixed and moving pivot loci - are input for a search algorithm that down selects a mechanism solution that satisfies transmission angle conditions, Grashof conditions, and a mechanism compactness condition. The final output of the presented method is planar four-bar motion generator that approximates prescribed coupler poses with satisfactory crank deflection and without follower buckling and also satisfies conditions for link rotatability, transmission angle and compactness.

Original languageEnglish (US)
Pages (from-to)245-253
Number of pages9
JournalProceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics
Issue number3
StatePublished - Sep 1 2009

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Mechanical Engineering


  • Buckling
  • Coupler force
  • Elastic deflection
  • Motion generation
  • Selection algorithm


Dive into the research topics of 'Four-bar motion generation with elasticity constraints and optimization'. Together they form a unique fingerprint.

Cite this