The authors develop simple, configuration-independent bounds for the Jacobian and the higher order derivatives of the forward kinematic map of a manipulator with revolute and prismatic joints. In doing so they obtain: a simple formula for the higher order derivatives of the forward kinematic map; an easily computable and meaningful metric on the group of rigid-body motions; and useful norms on the joint space of a manipulator. The bounds on the forward kinematic map are practical to implement and have proved to be very useful for trajectory interpolation, space generation, and interpolation of the robot dynamics. >