# Split Kinematics Without Abbé Offset Problems

How can four points be good Kinematics? For anyone who has tried to level a four-legged table their answer will probably be that it is impossible. The subtle principals behind the excellent performance of all kinematic couplings is the fundamental nature of spherical geometry and the self aligning nature of three contacts. The simple fact is that every point on the periphery of a sphere has a common point axis. When balanced vector forces are applied to the surface of a sphere the resultant of those forces manifests itself at this point axis. When working with Kinematic couplings you can toy with the surfaces that transfer the forces to the spheres almost at will, but if you expect predictable results you dare not mess with the spheres themselves.

The question then is how can we split the Kinematic system to steady a clumsy platform that is unstable? If we believe that we can cheat almost at will with the force drivers then we can take a simple element like a Vee Block or Parallel Cylinders, saw it down the middle, spread the pieces and we are in. The problem of course is how can we do our thing on the spherical part of the coupling? Using two small spheres or cutting a sphere in half and spreading the parts out until they contact the separated walls of the Vee Block will leave us with alignment and positioning problems that would make you wish that you had opted for a plain prismatic design in the first place. The answer is to simply go back to the principles.

If the target surfaces of the split Vee Block are four inches apart then we need a single sphere that will be tangent to these surfaces. But a four-inch or larger ball is far too big, too heavy and too expensive to be practical. From the discussion so far, a viable solution is deducible. All that is needed is two small spherical segments with the proper spherical radius rigidly mounted tangent to the faces of the split Vee Block.

The method of attachment will dictate the actual design perimeters of these spherical segments with the only constraints being their radius of curvature and that their tangent contacts bisect at the appropriate spherical radius. The split kinematic system is not very forgiving. For this reason, the dimensions must be machined very precisely, or two of the spherical contacts should be made adjustable. See Address Spheres in our kinematic product section. This is presented for basic design information of how to do it as the component, for each design must be custom manufactured. Our large array of spherical lapping tools assures fast delivery of these custom components.

Part # Description Price Purchase
SPVB SPLIT VEE BLOCK \$29.75
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