Page 127 - Robotics Designing the Mechanisms for Automated Machinery

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Kinematics and Control of

Automatic Machines

4.1 Position Function

We begin our discussion with the study of case 4, described in Chapter 1 and shown
in Figure 1.5. The drive, whatever its nature, imparts the required movement to the
tools through a mechanical system that controls the sequence and regularity of the
displacements. Every mechanism has a driving link and a driven link. The first ques-
tion in kinematics is that of the relationship between the input (driving motion) and
the output (driven motion). Let us denote:
x = the input motion, which can be linear or angular,
5 = the output motion, which also can be linear or angular.
Thus, we can express the relationship between these two values as:

We call Il(jt) the position function.
From Equation (4.1), it follows that

and

The importance of Equation (4.2) is that it expresses the interplay of the forces: by
multiplying both sides of Equation (4.2) by the force (or torque, when the motion is

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