Bal-tec™ Home Psuedo Kinematics

There are a number of very effective coupling designs that are not truly Kinematic. If the flat plane in contact with a ball is split and the two sections are inclined, we get a vee block. If we continue to incline the two planes, we will get more and more positive constraint of the ball. If we incline the two surfaces until they are perpendicular to the base plane and have the same spacing as the ball diameter, we have a device that will restrict two degrees of freedom. This doesn't seem very impressive until we pay notice to the fact that the bottom of the sphere will end up resting on the base plane that supports the two perpendiculars, so we get one more degree of constraint. If we machine a much larger spherical radius or even a flat plane on the bottom of the sphere we get a device that is very deterministic, along with huge load carrying characteristics.

If we take a ball conical cup with its three degrees of constraint and decrease the angle of the cone, we will get a more and more positive constraint of the sphere. If we incline the included angle of the surface until it is zero degrees, we have an internal cylinder. If this I.D. (Internal Diameter) cylinder is the same diameter as the ball, we have a device that will constrain two degrees of freedom. Without repeating all of the details of the previous example with the sphere resting against the base plane, we have a device that will very deterministically constrain three degrees of freedom and have enormous load carrying capacity.

It should be noted that both of the above couples constrain pitch, so when they are used together there is still complete reedom in the roll axis that will require a third couple if constraint of all six degrees of freedom is required. To eliminate backlash when the mass of these devices tries to move and elastic deformation occurs, a small preload should be placed on the ball. This mechanical bias is provided by making the dimensional spacing of the two parallel flat surfaces slightly less than that of the ball diameter and by making the inside diameter of the cylinder slightly smaller than it's matching ball diameter. We are in effect providing a light press fit.

We might say that neither of these devices are truly Kinematic because they are over constrained, but that might not make the best arrangement when you allow for the effect of elastic deformations of a classical kinematic system that is caused by a heavy applied load.

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