Maciejewski's Ill-Conditioned Equations of Motion paper This paper shows how ill-conditioned motion can arise as a result of solving kinematic equations, and gives a formula for approximating the degree of severity in a given situation. They also present an overview of the problem itself. The problem is that for a given hierarchical model, some small positional motions require large angular changes (the so-called ill-conditioned problem). They don't solve the problem completely (it can't always be solved), but they show that by damping singular values, they can resolve discontinuities at a singularity. Key ideas: By first identifying singularities, and then damping them, smoother motion can be achieved. Contributions: A well-conditioned IK solution. A formula for identifying the condition number (worst-case bound on relative error) in a transformation.