Building giant heavy structures that must be kinematically supported presents some major problems. The required load carrying capacity of the spherical elements of the kinematic coupling is the major limiting factor. Directly related to this is the very high load placed on the mating surfaces that are in contact with the spherical elements.

The use of large diameter spheres or large diameter spheres made of very stiff materials is an excellent approach; but this can only be taken so far, and these structures become so bulky that they aren't at all practical.

The not so simple solution to these

opposing problems is to construct kinematic

elements that consist of segments or slices of a very large spherical diameter or ellipses.

By building these spherical devices as compact monoliths that consist of two sections of a large spherical diameter, which are inset from the normal centerline, but with a common axis of symmetry, the job can be done.

An ultra fine grain, high chrome, high carbon, stainless steel that is hardened to 58 HRC minimum, is the material of choice, because of its high quality and for economic reasons.

Cemented Tungsten Carbide ( TC ) would provide far superior results, but at a much greater expense and longer lead-time.

The "Canoe Sphere" ( part number 2000-CS ) is a cylindrical post-mounted device that is now a catalog item.

Like many of our other Kinematic designs, the center hole of the cylindrical post is threaded for M10 X 1.5 for clamping from the rear. As an alternative clamping method, it also has a 5/16-inch (0.3125", 8 mm) counter bored hole through the length of the post, so that it can be held in place with a 5/16-inch (0.3125", 8 mm) diameter socket head cap screw from the front.

There is a dowel-pin hole off to one side, but exactly on the centerline of the post. Using this dowel-pin hole as a reference datum, the Canoe Sphere can be precisely located in a system, for interchangeability.

The large spherical diameters are precision ground using this dowel-pin hole as a datum.

The surface texture generated by the spherical grinding operation has a lay that is parallel to the axis of the cylindrical post so it is in line with the engaging surfaces, to give it superior repeatability.

The Canoe Sphere is built on a two-inch diameter circle. The three-quarter inch (0.75", 19 mm) diameter, one half inch ( 0.5", 12.7 mm) long post, is precision ground to plus nothing, minus .0005 inches (0.013 mm). The adjacent flange is precision ground flat and square, to the diameter of the post.

Canoe Sphere with Vee Block

The spherical diameters ground on the segments of the Canoe Sphere are 39.4 inches, which is one meter.

When used in conjunction with our large 90-degree vee block (our part number 2000-VB-CPM), each canoe sphere ( Part Number: CS-2000) will safely support 5000 pounds.

When using the Canoe Sphere and Vee block, there are no loose pieces. This is of special importance in airborne applications.

Use a 5/16" (8 mm) hexagon socket head cap screw for top mounting. For bottom mounting, use M10 X 1.5 hexagon socket head cap screws.

When the very ultimate in repeatability is required, spherical diamond kinematic components are the answer.

We have measured repeatability of a high quality sphere in a three diamond kinematic coupling at less than one half of a microinch (12.5 nanometers). Depending on whose research you read natural diamond has a stiffness or Young's Modulus of Elasticity somewhere around 900,000,000 P.S.I., which makes it by far the most rigid substance available.

In order to provide the very rigid structural loop required for nanometer (submicroinch) resolution, a one eighth of a carat gem quality diamond is brazed into a tungsten carbide substrata. This T.C. disk is three eighths of an inch ( 3/8", 9.5mm) diameter by one quarter of an inch ( 1/4", 6.4mm) thick. It is recessed on the backside to leave an annular ring around the edge. This annular ring is lapped within one light band. There is a #10-24 threaded hole in the center of the backside to hold this disk rigidly on the Kinematic Platform. The diamond is ground and polished to a rather large three sixteenth of an inch ( 3/16", 4.8mm) spherical radius, which is equivalent to a three eighths of an inch ( 3/8", 9.5mm) diameter ball.

One form of kinematic system to utilize these devices is three tungsten carbide cylinders and six of the spherical diamonds.Another configuration has one tungsten carbide ball, one tungsten carbide cylinder and one of the spherical diamonds on one of the platforms.

The other platform has a three-diamond nest to mate with the T.C. ball, a two-diamond cradle to locate the T.C. cylinder and a flat T.C. disk to mate with the spherical diamond.

Glue these components into counterbores for best results.

The Three Ball Kinematic Coupling is one of the top performing location devices. It restricts three degrees of freedom, without the distortion caused by clamping forces.

This three-ball device takes the place of the conical cup used in the classical kinematic system. However a three-ball system is limited to rather light load as the overall size of the coupling grows dramatically when larger balls must be used to cope with heavier payloads.

The solution in high load situations is to use a Rose Bud configuration. By cutting cylindrical fingers out of the side of a large diameter ball, and then cutting this finger in half, a small super rigid component or rose petal is produced that is easy to mount on the Kinematic Platform.

To rigidly mount these components you simply machine a 120 degree "Y" shaped trench in the platform, with an end mill of a radius, that matches the cylindrical radius of the rose petal and glue the individual components in. Because the resulting force on the components is down and out and they are buried in the "Y" shaped trench, the limiting load factor is the strength of the material that the Kinematic Platform is made of.

The spherical surfaces of these components retain the high quality geometry and excellent surface finish of the precision balls that is was removed from.

To reduce the overall height of the assembly the tops of the cylindrical fingers are usually cut down some.

These devices can be prepared for surface mounting by drilling and threading a hole in the base plane. When this is done, much of the systems rigidity is lost.

A single standard component has been developed that will fill most kinematic applications. A three eighths of an inch ( 3/8", 9.53mm) radius, that is three three quarters of an inch ( 3/4", 19mm ) diameter cylinder is cut out of a one and one quarter inch ( 1 1/4", 3.175mm ) diameter sphere. This cylindrical finger is then cut in half. The nest provided by three of these components is compatible with any ball size from three eighths of an inch ( 3/8", 9.53mm ) to over one inch ( 1", 25.4mm ) diameter.

The material usually used for manufacturing these components is tungsten carbide. This is the stiffest, hardest commercially available material with a Young's Modulus of Elasticity of 98,000,000 P.S.I. and a hardness of 91 HRA.

They are also available in a micro grained stainless steel that is hardened to 58 HRC minimum.

Other combinations of radii and material will be produced to fill any specific customer needs. These include corrosion resistance and special magnetic or electrical properties.