Page 150 - Mechatronics with Experiments

136 MECHATRONICS
3. Backlash: there is always an effective backlash in motion transmission mechanisms.
The backlash is given in units of arc minutes = 1∕60 degrees in rotary mechanisms,
and in inches or mm units in translational mechanisms. Notice that backlash directly
affects the positioning accuracy. If the position sensor is connected to the motor,
not to the load, it will not be able to measure the positioning error accurately due
to backlash. Therefore, if backlash is large enough to be a concern for positioning
accuracy, there has to be a position sensor connected to the load in order to measure
the true position, including the effect of backlash. In such systems, it is generally
necessary to use two position sensors (dual sensor feedback, or dual loop control):
one position sensor connected to the motor and the other position sensor connected
to the load. The motor-connected sensor is primarily used in the velocity control
loop to maintain closed loop stability, whereas the load-connected sensor is primarily
used for accurate position sensing and control. Without the motor-connected sensor,
the closed loop system may be unstable. Without the load-connected sensor, desired
positioning accuracy cannot be achieved. In systems where the backlash is much
smaller than the positioning accuracy required, the backlash can be ignored.
4. Stiffness: the transmission components are not perfectly rigid. They have finite stiff-
ness. The stiffness of the transmission box between input and output shaft is rated
with a torsional or translational stiffness parameter.
5. Break-away friction: This friction torque (or force) is an estimated value and highly
dependent function of the lubrication condition of the moving components. This is
the minimum torque or force needed at the input shaft to move the mechanism.
6. Back driveability: Motion conversion mechanisms involve two shafts, the input shaft
and output shaft. In the normal mode of operation, the motion and torque in the
input shaft are transmitted to the output shaft with a finite efficiency. Back driveablity
refers to the transmission of power in the opposite direction, that is the motion source
is provided at the output shaft and transmitted to the input shaft. Most spur gear,
belt and pulley type mechanisms are back driveable with the same efficiency in
both directions. Rotary-to-linear motion conversion mechanisms such as lead-screw
and ball-screws have different efficiencies and are not necessarily back driveable.
Ball-screws are considered back driveable for all cases. The back driveability of a
lead-screw depends on the lead angle. If the lead angle is below a certain value (i.e.,
◦
30 ), the back driveability may be in question. Furthermore, it also highly depends on
the lubrication condition of the mechanism since it affects the friction force that must
be overcome in order to back drive the mechanism. Worm-gear mechanisms are not
back driveable. There are applications which benefit from that, such as raising a very
heavy load and in the case of power failure in the input shaft motor, the mechanism is
not supposed to back drive under gravitational force and is suppose to hold the load
in position. In short, when back driveability is required, two variables are of interest:
(i) efficiency in the back drive direction, and (ii) F friction force to overcome
b fric
in order to initiate motion, which is highly dependent on the lubrication conditions.

3.2 ROTARY TO ROTARY MOTION
TRANSMISSION MECHANISMS

3.2.1 Gears
Gears are used to increase or decrease the speed ratio between the input and output shaft.
The effective gear ratio is obvious (Figure 3.1). Assuming that the gears do not slip, the