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

• A procedure is developed for designing rigid-body, shape-changing mechanisms.
• A chain of rigid bodies can be repositioned to approximate any number of curves.
• The chain contains revolute and prismatic joints to match different length curves.
• Theory is generated to compare contiguous sets of points among curves.
• A process identifies the ideal shape for the rigid bodies and joint type/locations.

This paper presents a kinematic procedure to synthesize planar mechanisms capable of approximating a shape change defined by a general set of curves. These “morphing curves,” referred to as design profiles, differ from each other by a combination of displacement in the plane, shape variation, and notable 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. A method is presented to iteratively search along the profiles for locations that are best suited for prismatic joints. The result of this methodology is the creation of a chain of rigid bodies connected by revolute and prismatic joints that can approximate a set of design profiles.