The Fij are calculated from a static force analysis of the linkage. Dynamic forces
can be much greater than static forces if speeds are high. However, if this static force
transmission index indicates a problem in the absence of any dynamic forces, then the
situation will obviously be worse at speed. The largest joint force at each position is used
rather than a composite or average value on the assumption that high friction in anyone
joint is sufficient to hamper linkage performance regardless of the forces at other joints.
Equation 11.23a is dimensionless and so can be used to compare linkages of different
design and geometry. Equation 11.23b has dimensions of reciprocal length, so caution
must be exercised when comparing designs when the external load is a torque. Then
the units used in any comparison must be the same, and the compared linkages should
be similar in size.
Equations 11.23 apply to anyone instantaneous position of the linkage. As with the
transmission angle, this index must be evaluated for all positions of the linkage over its
expected range of motion and the largest value of that set found. The peak force may
move from pin to pin as the linkage rotates. If the external loads vary with linkage position,
they can be accounted for in the calculation.
Holte and Chase suggest that the IPI be kept below a value of about 2 for linkages
whose output is a force. Larger values may be tolerable especially if the joints are designed
with good bearings that are able to handle the higher loads.
There are some linkage positions in which the IPI can become infinite or indeterminate
as when the linkage reaches an immovable position, defined as the input link or input
joint being inactive. This is equivalent to a stationary configuration as described in
earlier chapters provided that the input joint is inactive in the particular stationary configuration.
These positions need to be identified and avoided in any event, independent
of the determination of any index of merit. In some cases the mechanism may be immovable
but still capable of supporting a load. See reference [1] for more detailed information
on these special cases.