In the design of spatial linkages, the finite-position kinematics is fully specified by the position of the joint axes, i.e., a set of lines in space. However, most of the tasks have additional requirements regarding motion smoothness, obstacle avoidance, force transmission, or physical dimensions, to name a few. Many of these additional performance requirements are fully or partially independent of the kinematic task and can be fulfilled using a link-based optimization after the set of joint axes has been defined. This work presents a methodology to optimize the links of spatial mechanisms that have been synthesized for a kinematic task, so that additional requirements can be satisfied. It is based on considering the links as anchored to sliding points on the set of joint axes, and making the additional requirements a function of the location of the link relative to the two joints that it connects. The optimization of this function is performed using a hybrid algorithm, including a genetic algorithm (GA) and a gradient-based minimization solver. The combination of the kinematic synthesis together with the link optimization developed here allows the designer to interactively monitor, control, and adjust objectives and constraints, to yield practical solutions to realistic spatial mechanism design problems.

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