Continuous Approximate Synthesis of Planar and Spatial Mechanisms

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Mechanism synthesis is an important branch of mechanism science that has developed over the last millennium. A mechanism is a collection of interconnected components individually called links. The connection between two adjacent links is a joint. Four-bar linkages are an important class of mechanism that consist of a relatively fixed rigid link to which an input and an output link are attached, typically by rotary, or linear joints. The input and output links are additionally connected to a fourth link which couples the motion of the input to that of the output, forming a closed loop. Four-bar linkages have important applications to function generation (the motions of the input and output links are coordinated according to an algebraic function), rigid body guidance, and trajectory generation. The current approach is to prescribe a finite set of positions and orientations of the coupler, link 4, or a finite set of values for pairs of input and output link angles, and then to use numerical procedures to synthesise the geometry of a linkage that can approximate the desired motions with the least error, but relative to only the prescribed values. This is termed