Digital three-dimensional (3D) models are useful for biomechanical analysis because they can be interactively visualized and manipulated. Synthesizing and analyzing animal locomotion with these models, however, is difficult due to the large number of joints in a fully articulated skeleton, the complexity of the individual joints, and the huge space of possible configurations, or poses, of the skeleton taken as a whole. A joint may be capable of several biological movements, each represented by a degree of freedom (DOF). A quadrupedal model may require up to 100 DOFs to represent the limbs and tnmk segments only, resulting in extremely large spaces of possible body configurations. New methods are presented here that allow limbs with any number of biomechanical DOFs to be kinematically exercised and mapped into a visualization space. The spaces corresponding to the ranges of motion of the left and right limbs are automatically intersected and pruned using biological and locomotion constraints. Hind and fore spaces are similarly constrained so that Genetic Algorithms (GAs) can be used to quickly find smooth, and therefore plausible, kinematic quadrupedal locomotion paths through the spaces. Gaits generated for generic dog and reptile models are compared to published gait data to determine the viability of kinematics-only gait generation and analysis; gaits generated for Apatosaurus, Triceratops, and Tyrannosaurus dinosaur models are then compared to those generated for the extant animals. These methods are used for several case studies across the models including: isolating scapulothorax and shoulder joint functionality during locomotion, determining optimal ankle heights for locomotion, and evaluating the effect of limb phase parameters on quadrupedal locomotion.