An approach to constrained time-efficient and smooth cubic spline trajectory generation is presented. A suitable objective function to combine the minimisation of travelling time with smoothness of the robot trajectories is proposed. Cubic splines are used to describe the joint trajectories which satisfy constraints on velocity, acceleration and jerk. The algorithm combining the penalty function and polytope method is developed and used to find the globally optimal solution to the optimisation problems. Minimisation of the energy, the vibrations and the mechanical wear of the robotic system is also explained intuitively. The effects of the weights in the objective function and of control knots on smoothness, time optimality and path deviation errors are shown mainly by simulation. The simulation results also show that path deviation errors can be reduced through suitably choosing the weights in the objective function and all the joint trajectories are optimised in terms of the objective function, whereas a solely time-efficient trajectory generation scheme only fully utilises the slowest joint capabilities. The feasibility of the method is further illustrated by experimental results with a SCARA type robot.