Massless Cable for Real-time Simulation

A technique for real-time simulation of hoisting cable systems based on a multibody nonideal constraint is presented. The hoisting cable constraint is derived from the cable internal energies for stretching and twisting. Each hoisting cable introduces two constraint equations, one for stretching and one for torsion, which include all the rigid bodies attached by the same cable. The computation produces the global tension and torsion in the cable as well as the resulting forces and torques on each attached body. The complexity of the computation grows linearly with the number of bodies attached to a given cable and is weakly coupled to the rest of the simulation. The nonideal constraint formulation allows stable simulations of cables over wide ranges of linear and torsional stiffness, including the rigid limit. This contrasts with lumped element formulations including the cable internal degrees of freedom in which computational complexity grows at least linearly with the number of cable elements – usually proportional to cable length – and where numerical stability is sensitive to the mass ratio between the load and the lumped elements.