This paper presents a kinematic synthesis methodology for planar shape-changing rigid-body mechanisms that addresses constraints arising in the design of variable-geometry polymer extrusion dies. Such a die is capable of morphing its orifice in order to create extrusions of non-constant cross section. A variable-geometry shape-changing die problem is defined by a set of design profiles of different shapes and arc lengths, which approximate various cross sections of the extrusion. The primary advantage of the presented methodology is addressing the need for bodies in the mechanism formed by fusing links in the shape-changing portion of the chain. Previous methodologies included such fused links, but only at the end of the synthesis process where revolute joints were seen to be underutilized. A new method is needed to control, or even eliminate the use of revolute joints in the shape-changing chain of rigid links. The result of this new work is an iterative method which generates an optimized morphing chain to best match the design profiles while minimizing the number of prismatic and revolute joints needed to do so. The additional variable-geometry design constraints also require a generalization to the definition of fixed-end profiles previously proposed, also allowing chain ends to be defined by prismatic joints on a fixed line of slide. A virtual-chain method is also proposed to solve closure problems caused by the reduction in the number of revolute joints.
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