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Methods of joint trajectory generation for mechanical manipulators using X-spline and quartic spline functions are presented. A sequence of Cartesian knots, i.e. positions and orientations of the hand, are selected from the desired Cartesian path. Joint values corresponding to these selected knots are solved from the kinematic equation. Approximate joint paths are constructed by interpolating these joint positions. At any instant, two or more future knots need to be known in advance in order to determine the current joint trajectories. Approximate errors for Cartesian paths are discussed. An illustrative example is used for comparing these trajectories to other existent polynomial-type trajectories.