Four-bar linkage synthesis for a combination of motion and path-point generation

Date of Award


Degree Name

M.S. in Mechanical Engineering


Department of Mechanical and Aerospace Engineering


Advisor: Andrew P. Murray


This thesis develops techniques that address the design of planar four-bar linkages for tasks common to pick-and-place devices, used in assembly and manufacturing operations. The analysis approaches relate to two common kinematic synthesis tasks, motion generation and path-point generation. Motion generation is a task that guides a rigid body through prescribed task positions which include position and orientation. Path-point generation is a task that requires guiding a reference point on a rigid body to move along a prescribed trajectory. Pick-and-place tasks often require the exact position and orientation of an object (motion generation) at the end points of the task. Within the range of movement, the motion restrictions are less rigorous with only the position of the object (path generation) being specified to either avoid obstacles or provide direction for a suitable path. Established synthesis theory has been developed for either motion generation or path-point generation tasks. This thesis presents four-bar linkage synthesis methods for tasks that include a combination of motion and path-point generation. This synthesis challenge is addressed via two approaches: Geometric Constraint Programming (GCP) and numerical solutions to synthesis equations. Using GCP, a step-by-step methodology has been established to find solutions to these synthesis challenges. This technique provides a synthesis process that is intuitive, visual, and avoids the need for the designer to engage in solving complex equations, The drawback to kinematic synthesis using GCP, however, is that only one linkage solution is obtained and sketched by the designer. Using numerical methods, techniques are presented to formulate the kinematic chain constraint equations and solve for the appropriate link lengths and pivot locations. Numerical solutions are generated by the Bertini software package, a program that supports the calculation of large polynomial equations set. Examples of various combinations of motion and path point generation are presented.


Automation Mathematical models, Assembly-line methods Mathematical models, Machinery, Kinematics of, Mechanical engineering; motion generation; path-point generation; pick-and-place; combination of motion and path-point generation; geometric constraint programming

Rights Statement

Copyright © 2013, author