Development of Planar, Shape-changing Rigid Body Segmentation Process for General Design Profiles
This work describes the early segmentation results in the progress of a mechanism design process to produce simple planar machines that could approximate a shape change defined by a set of curves with significant differences in arc length. The design profiles vary from one another by a combination of rigid-body displacement and shape change that includes significant differences in arc length. Where previous rigid-body shape-change work focused on mechanisms composed of rigid links and revolute joints to approximate curves of roughly equal arc length, this work introduces prismatic joints into the mechanisms in order to produce the different desired arc lengths. The first step is to convert the design profiles into piecewise linear curves, referred to as target profiles. The piecewise linear representation that proves most useful has points identified along the curve at roughly equal distances. The second step is to compare segments of the target profiles seeking those that are best approximated by a common rigid body and those that share curvature similarities allowing for the introduction of a prismatic joint. In the end, a chain of rigid bodies that are joined by pin and prismatic joints can be produced. The chain can closely estimate the shape of a set of design profiles.
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