Kinematic synthesis of planar, shape-changing rigid body mechanisms for design profiles with significant differences in arc length

Date of Award


Degree Name

Ph.D. in Mechanical Engineering


Department of Mechanical and Aerospace Engineering


Advisor: Andrew P. Murray


Design of shape-changing machinery is an area of growing significance. Shape-change may be employed in the near future to vary the cross section of a wing, create flow-field control by altering shapes to locally affect downstream fluid behavior, or vary the size of a car seat to meet a wider array of ergonomic needs. Rigid body shape-change mechanisms offer many advantages including the high capacity to endure substantial loads while achieving large displacements. Their design techniques are also well-established. The goal of this research project is to develop the synthesis theory to address planar rigid-body shape-change where significant differences in arc length define the problem. This dissertation presents a process to approximate several design profiles of significantly different arc lengths with rigid bodies connected by revolute and prismatic joints. This process is referred to as segmentation, and the initial step is the conversion of the design profiles into piecewise linear target profiles. Any two contiguous points on a target profile define a piece. Target profiles have the same approximate piece-length throughout. This is followed by segmentation which serves to identify the contiguous sets of pieces that are best approximated by either a rigid body M-segment or a constant curvature C-segment that contains a prismatic joint. To facilitate segmentation, the concept of segment matrix is introduced. A segment matrix identifies the lengths of the bodies in the sequence of M- and C-segments along a profile. The segmentation process is applied to open, closed, and fixed-end design profiles. A MATLAB-based tool was developed to facilitate visual assessment of the process and results. Finally, this dissertation illustrates five mechanization examples that apply the segmentation process, and the fundamental mechanism synthesis to guide the motion of the chain of rigid bodies to progress to the subsequent positions.


Piecewise linear topology, Structural optimization, Mechanical engineering; morphing machines; rigid-body shape-change; planar mechanisms; profile segmentation; design and target profiles; different arc lengths

Rights Statement

Copyright 2013, author