Over many size and time scales, behaviors such as locomotion or feeding require mechanical movements. Size and time in turn determine a behavior’s dominant mechanical properties: mass, stiffness or viscous damping. The constraints for limbed behaviors can thus be quantified by two variables: limb size and limb speed, defining a ‘mechanics space’ that shows the relative magnitude of each mechanical property for animals ranging from fruit fly to elephant. The mechanics space has three distinct regions: 1) an inertia-dominated region; 2) a gravity or elastic-force-dominated region; and 3) a viscous-force-dominated region. In the mass-dominated region, associated with large limbs moving rapidly, muscle work is translated into primarily kinetic energy. Thus, stable motion requires compensatory control and active damping. In the elastic-force-dominated region, associated with small limbs moving slowly, muscle energy is translated into primarily gravitational or elastic potential energy. Thus, compensatory control and active damping are unnecessary. Lastly, in the viscous region, associated with small limbs moving quickly, joint viscosity acts to damp actuation, resulting in exclusively stable movements. Control and stability of a limb thus depends almost entirely on the size and speed of limb movement, and this has fundamental implications for neural control.