Page 129 - Robotics Designing the Mechanisms for Automated Machinery

118 Kinematics and Control of Automatic Machines

A scheme of this mechanism is presented on the left side of the figure. Here 0 :A = r
for the driving link at the very moment of engagement, and OjA' = r is constant at all
intermediate times. The number of slots n in the cross determines the angle y/ 0, i.e.,

and, obviously,

From the triangle O^A we obtain

Applying Equation (4.8) to the triangle 0^^' we can express

where the value of if/ is unknown, and the length of 0^' = h.
From the sine law, we obtain

And thus from Equations (4.9) and (4.10):

Denoting A = r// and simplifying Equation (4.11), we obtain

or

From Equation (4.13) we obtain the following expression for the velocity of the driven
link ij/:

or