Compliant mechanism synthesis using degree of genus and variable width curves

Compliant mechanisms (CMs) utilize elastic deformations for mechanism functions. Their merits primarily come from jointless structures. The structure of a fully CM is a piece of elastic material and is defined by its topology, shape and size. Topology is the overarching material layout of a CM while shape and size are on its structural details, but topology is entangled with shape and size in the synthesis process of a CM because its elastic deformation is from the joint effect of topology, shape and size. Degree of freedom (DOF) and number of links used in rigid mechanism synthesis are not effective to guide the synthesis of CMs since any point of a fully CM can deform and its whole structure forms a single piece. Without effective synthesis guidance, the structural complexity of a synthesized CM can be undesirably high. In this thesis, degree of genus (DOG) was introduced for topology guidance of CM synthesis. DOG of a CM is the number of holes and is actively controlled during its synthesis process. With DOG guidance, a synthesized CM will not have overcomplicated topology. Variable width curves (VWCs) was introduced in this thesis for shape and size description. Any connection in a CM is defined as a VWC and the entire CM is modeled as a network of VWCs. With VWC description, a synthesized CM will not have unsmooth connection. Under DOG and VWC strategies, CM synthesis is systematized as optimizing control parameters of networks of VWCs. The proposed CM synthesis using DOG and VWC strategies was demonstrated by synthesizing shape morphing compliant mechanisms