The paper addresses the global minimum-time trajectory planning of an m-joint mechanical manipulator. Using a joint space scheme with given intermediate points to be interpolated by piecewise cubic polynomials, a novel bisecting-plane algorithm is proposed to schedule the times between adjacent knots under velocity, acceleration, and jerk constraints. This algorithm, which is proved to be globally convergent with certainty within an arbitrary precision, uses an interval procedure (a subroutine adopting tools and ideas of interval analysis) in proving that a local minimum is actually a global one. A worked example for the six-joint case is exposed, and computational results of a C++ implementation are included.