Capstan/wippen heel intersection

[Clark]

Hi,

Just a quick response to a line in Richard Brekne's post:

> From a friction standpoint, and I believe from a leverage standpoint.. the
> capstan /cushion should act as nearly like to a pivot as is possible.

The intersection is less like to pivots than gear or cam action. In
order for one to drive the other the respective vectors of velocity
_commonly tangent to the capstan and heel at the points of contact_ are
equal in magnitude and direction; however, their motion is angular and
the _actual_ instantaneous velocities are perpendicular to the lines
from these points to the respective action centers. The difference
between the pairs of actual velocities is the instantaneous velocity of
sliding between the profiles, and which should be smallest around the
line between the two centers. An interesting note, though:

> The energy lost in friction at the teeth [action part contact profiles] 
> and at the bearings is...less during recess [above the line between 
> centers] than during approach [below it]...During approach the teeth [parts], 
> while sliding on each other, are pushing into mesh, while during recess 
> they are drawing out of mesh. Gears [actions] would therefore be more 
> efficient and durable if the action were confined to recess.

	p236. Albert, C.D. & F.S. Rogers. "Kinematics of Machinery"

The path of the point of contact is a function of the profiles of the
parts, compounded a little in this case by nonlinearities of heel
padding and compression over time (oh, and the deformation of keys under
load); for one, involute profiles have been favored for gear teeth
because they can tolerate changing geometry. Anyways, a more efficient
action also is a more durable action.

Regards,


Clark