There are three general tasks for dimensional synthesis, i) path generation, in which the trajectory of a point in the output link is required, ii) motion generation, in which the trajectory of the output link is required, and iii) function generation in which the movement of the output link relative to an input link is required. The equations for function generation can be obtained from those for motion generation by considering the movement of the output link relative to an input link, rather than relative to the base frame.