Burmester’s solution to the problem of guiding a body through four precision points has been extended to find planar mechanisms that have their pivots located inside prescribed regions. The complex number formulation has been used to generate the Burmester curves. A random search technique was developed to choose a new set of precision points that lie within user specified limits, in order to find a set of curves that pass through the desired regions. A computer program was written to generate Burmester curves that lie within the desired regions, while maintaining a coupler motion within satisfactory limits. An automobile suspension linkage was successfully designed using this program.