1. Trajectories for robotic arms can include via points that the arm passes close to but not necessarily through. Both position and orientation of the arm need to be interpolated along the trajectory. 2. Transitions between straight line segments of a trajectory involve constant acceleration curves like parabolas. The trajectory is planned to satisfy constraints like initial and final positions, velocities, and times. 3. Rotational transitions between orientations are found similarly by defining equivalent axes of rotation and making the rotation a linear function of time along the transition.