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456 CAM DESIGN HANDBOOK

14.2 ROLLING BODIES

Let us now define the term pure rolling as the action on a surface in which the points on
the first body consecutively contact only one corresponding point on the second body; see
Fig 14.3. If every point on the first body comes in contact with the same point on the
second body, we have pure sliding. In Fig. 14.3, for pure rolling to occur between con-
tacting bodies B and C, the arc QW must equal the arc PX if W meets X during the action.
Also from Eq. (14.1) and Fig. 14.2 for pure rolling V P/Q = 0, V P/A and V P/Q are colinear and
the point of contact PQ is on the line of centers O 1O 2 at times.
By constructing on approximation, let us find the contour of the body B having pure
rolling action with given body C. Body C drives clockwise with the initial contact Q on
the line of centers. Both bodies turn through a small angle. The steps for construction are
as follows:
1. To find point a¢ on body B corresponding to point a on body C, swing arc 0 1a to line
of centers, giving point R.
2. With radius 0 2R, draw arc RS.
3. Since arc length Pa¢ is equal to arc length Q a, use chord Q a as a compass distance and
draw an arc from P intersecting arc RS, giving point a¢.
4. Find b¢ on C which contacts b on B as in steps (a) and (b). Obtain U on the line of
centers by swinging arc 0 1b and draw arc UV of radius 0 2U.
5. Arc ab equals arc a¢b¢. Use chord ab as a compass distance to draw arc a¢b¢ from a¢,
intersecting arc UV and giving point b¢.
6. Repeat to find other points.
Note that, if body B were driven in translation, we would have RS and UV as lines
perpendicular to 0 10 2 since arcs RS and UV would have infinite radii.

FIGURE 14.3. Pure rolling between bodies in contact.