Motion-synthesis problems arise in the creation of physically realistic animations involving autonomous characters. Trpically characters are required to perform goal tasks, subject to physical law and other constraints on their motion. Witkin and Kass (1988) dubbed this class of problems “Spacetime Constraints“ (SC) and presented results for specific problems involving an articulated figure. Their approach was based on a procedure for the local optimization of an initial approximate trajectory supplied by the user. Unfortunately, SC problems are typically multimodal and discontinuous, and the number of decision alternatives available at each time step can be exponential in the number of degrees of freedom in the system. Thus, constructing even coarse trajectories for subsequent optimization can be difficult. We present an algorithm that constructs such trajectories de novo , without directive input from the user. Rather than use a time-series representation, which might be appropriate for local optimization, our algorithm uses a stimulus-response model. Locomotive skills appropriate for the given articulated figure are acquired through repeated testing of (simulated) reality. Our initial implementation, which chooses stimulus-response parameters using a parallel genetic algorithm, succeeds in finding good, novel solutions for a test suite of SC problems involving unbranched 2-D linkages.