Kinematic synthesis and analysis techniques to improve planar rigid-body guidance

Date of Award


Degree Name

Ph.D. in Mechanical Engineering


Department of Mechanical and Aerospace Engineering


Advisor: Andrew Murray


Machine designers frequently need to conceive of a device that exhibits particular motion characteristics. Rigid-body guidance refers to the design task that seeks a machine with the capacity to place a link (or part) in a set of prescribed positions. An emerging research area in need of advancements in these guidance techniques is rigid-body, shape-change mechanisms. This dissertation presents several synthesis and analysis methods that extend the established techniques for rigid-body guidance. Determining link lengths to achieve prescribed task positions is a classic problem. As the number of task positions increases, the solution space becomes very limited. Special arrangements of four and five task positions were discovered where the introduction of prismatic joints is achievable. Once dimensions of link lengths are determined, solutions with defects must be eliminated. Defects include linkages that do not remain on the same assembly circuit, cross branch points where the mechanism cannot be driven, or achieve the task positions in the wrong order. To address the circuit defect, a general strategy was formulated that determines the number of assembly configurations that exist in a linkage and the sensitivity of the motion to a link length. To address the branch defect, extensible equations that generate a concise expression of the singularity conditions of mechanisms containing a deformable closed loop was developed. To address the order defect, an intuitive method to ensure that rigid-bodies will reach design positions in the proper order has been developed. The result of the dissertation is a suite of methodologies useful in the synthesis and analysis of planar mechanisms to accomplish rigid-body guidance.


Machinery, Kinematics of, Links and link-motion Mathematical models

Rights Statement

Copyright 2009, author