swivel ball/cone torque
swivel ball/cone torque
(OP)
trying to work out an adjustable swiveling foot.
Would like to clamp a ball between two cones (would be threaded together) as illustrated. Known would be the contact angles (and thus the radii of the contact rings), the compression force along the common axis of the cones, and the friction coefficients. It would seem that the torque necessary to rotate the ball coaxially to the foot and the torque necessary to swivel off-axis would be different from each other -- how would I best calculate the latter?
Thanks in advance.

Would like to clamp a ball between two cones (would be threaded together) as illustrated. Known would be the contact angles (and thus the radii of the contact rings), the compression force along the common axis of the cones, and the friction coefficients. It would seem that the torque necessary to rotate the ball coaxially to the foot and the torque necessary to swivel off-axis would be different from each other -- how would I best calculate the latter?
Thanks in advance.






RE: swivel ball/cone torque
-handleman, CSWP (The new, easy test)
RE: swivel ball/cone torque
My first thought is that, given Newtonian friction, the contact radius is smaller for axial rotation.
I see no problem applying thousands of pounds clamping force by tightening your thread. It will be easy to exceed material yield stresses at the contact points, making your friction definitely non-Newtonian. Consider a spring loaded contact point.
--
JHG
RE: swivel ball/cone torque
What does the through hole in the left housing do?
With 2 cones and the threads all fighting for location as defined by the sphere I picture some 3D jamming going on. Maybe that would be a good thing for your application. At some point I'd think about letting one cone float radially, or maybe replacing the cone in the left housing with a flat somewhat compliant surface.
https://www.carrlane.com/SiteData/FeatureImages/CL...
RE: swivel ball/cone torque
@ Handleman -- When the ball is rotated coaxially to a cone, I was thinking that if you broadened the line of contact a bit (as would actually happen in reality), it would be rather like a cone clutch (integration of concentric rings).
But when the ball is swivelled along any other axis, I'm thinking now that it might be an integration of cross-sections that would look like increasingly smaller cylinders pressed into increasingly smaller V-blocks?
RE: swivel ball/cone torque
The normal force at each point must pass through the sphere center. I think.
The integrals around the contact circles must somehow be a constant.
Simple thought experiment:
Consider a sphere resting inside a cone (point down, facing up)
If friction were directionally dependent there would be a clear preferred position. There is not.
RE: swivel ball/cone torque
The shaft has a radius that is smaller than the ball and a length that has to be greater than the radius of the ball so the leverage is much different.
OTOH turning the ball means the line of action has a variable radius about the axis of rotation, while twisting the ball means a smaller maximum radius that is constant.
Example: Set a sphere at X0, Y0, Z0 with the lever initially along the Z axis and a circle of contact in the X-Y plane.
Twisting the lever about the Z axis places all the points of contact as contributors to resisting torque with the radius of the sphere.
If the lever is moved towards the Y axis, rotating the sphere about the X axis, then the contact along the X axis will contribute no resistance because there's no leverage against rotation, while a point on the sphere at the Y axis will resist with leverage of the radius.
So I'm inclined to think some integration is involved to determine the transition from being similar to being as different as they would be in my example.
RE: swivel ball/cone torque
RE: swivel ball/cone torque
RE: swivel ball/cone torque