Robot Mechanisms and Mechanical Devices Illustrated - Profe Saul

Chapter 10 Manipulator Geometries 245
In order to put the slider crank to good use, a method of calculating
the position of the slider relative to the crank is helpful. The equation for
calculating how far the slider travels as the crank arm rotates about the
motor/gearbox shaft is: x = L cos Ø+ r cos Ø.
ARM GEOMETRIES
The three general layouts for three-DOF arms are called Cartesian, cylindrical,
and polar (or spherical). They are named for the shape of the volume
that the manipulator can reach and orient the gripper into any position—the
work envelope. They all have their uses, but as will become
apparent, some are better for use on robots than others. Some use all sliding
motions, some use only pivoting joints, some use both. Pivoting
joints are usually more robust than sliding joints but, with careful design,
sliding or extending can be used effectively for some types of tasks.
Pivoting joints have the drawback of preventing the manipulator from
reaching every cubic centimeter in the work envelope because the elbow
cannot fold back completely on itself. This creates dead spaces—places
where the arm cannot reach that are inside the gross work volume. On a
robot, it is frequently required for the manipulator to fold very compactly.
Several manipulator manufacturers use a clever offset joint
design depicted in Figure 10-3 that allows the arm to fold back on itself
Figure 10-3 Offset joint
increases working range of
pivoting joints