Page 262 - Robot Builders Source Book - Gordon McComb

250 Feeding and Orientation Devices

mation of it can be received when W= 0, neglecting friction.) This condition exists
during time t 2, which is defined as

The displacement S^ then is

Obviously, for the second half-period (section KM) we receive correspondingly (to
expressions a, b, c, and d) a set of following formulas:

This speed value is negative while friction force acts in the positive direction:

where W=-ju(g+S cr'smj3).
Summarizing these two slides we obtain the resulting displacement of the body
relatively to the tray in the bowl. A more precise description of the relative movement
of the body on the tray follows. We express the absolute coordinates of the body X and
Y in the following form:

where -x 0(f) and y 0(t) are coordinates of the tray; x and y are relative coordinates of
the body. Then, rewriting, (7.31) we obtain

For the case of dry friction we have F = -ji/ATsign x, and for the normal reaction on the
body correspondingly N = my 0 (t) + rag cos a.
Then the most important case of transportation without rebounds, the relative
motion of the body along the tray, becomes as follows:

TEAM LRN