A two part trajectory and speed planning procedure for a two-link rigid manipulator is presented. The planning is done at the joint level using cubic spline functions, and the trajectory of the robot is specified by a sequence of knots in space Cartesian coordinates. These knots are transformed into two sets of joint coordinates, and piecewise cubic spline functions are used to fit these two sets employing a time scale to construct an initial trajectory for the manipulator. Linear scaling of the time variable is used to accommodate the angular velocity and acceleration constraints imposed at the joint level. A new nonlinear time scaling scheme is then used for speed control so as to fit the manipulator’s tip velocity to a pre-specified profile. Simulation results for the manipulator with payload masses following a planned trajectory are presented.