This section describes how a control law that implements virtual fixtures can be derived. It is assumed that the robot is a purely kinematic device with end-effector position formula_1 and end-effector orientation formula_2 expressed in the robot's base frame formula_3. The input control signal formula_4 to the robot is assumed to be a desired end-effector velocity formula_5. In a tele-operated system it is often useful to scale the input velocity from the operator, formula_6 before feeding it to the robot controller. If the input from the user is of another form such as a force or position it must first be transformed to an input velocity, by for example scaling or differentiating.