Topology optimization of planar linkage systems involving general joint types

• The topology and dimension of planar linkage mechanisms are simultaneously synthesized.
• A new topology optimization method to deal with various joint types is proposed.
• The concept of double-springs to connect ground rigid blocks is newly introduced.
• Mechanisms with revolute, prismatic and pin-in-slot joints were successfully synthesized.

The simultaneous synthesis of the number and dimension of planar linkage mechanisms has opened a new possibility in mechanism synthesis. Mechanisms with revolute joints were a main concern so far but planar mechanisms with general joints including prismatic joints cannot be synthesized. This study aims to overcome the current difficult by proposing a new synthesis method. The key idea in the proposed approach is to parameterize joint types directly, unlike earlier methods parameterizing ground link skeletons connected by revolute joints. So, we propose a new concept of “double-springs” that can be used to connect a finite number of ground rectangular rigid blocks that discretize a given synthesis domain. Rigid blocks are elaborately connected by two sets of one-dimensional springs, i.e., double-springs and their stiffness values are varied by design variables. The connectivity of the double-springs dictated by the stiffness values determines the synthesized link mechanisms. We explain why it is crucial to use the double-spring concept for the synthesis of general joints such as prismatic joints. Various benchmark problems were considered to demonstrate the validity of the proposed method.