Gigantic Load Supporting Kinematic Structures

Kinematic couplings are usually thought of as petite systems used in lightly loaded instrument and gage applications, but they can also be applied in large heavily loaded situations. Loads of up to about 800 pounds (363 kg) work quite well with conventional Kinematic designs. A safe design at this level consists of three 2-inch diameter spheres made of high chrome, high carbon stainless steel that is hardened to 58 HRC, and three 90-degree vee blocks, made of the same material. The large balls used in this application are custom made for the desired mounting configuration. Above this load level, things have to change!

Increase the Ball Diameter

As the contact forces on the surfaces of the spheres are the limiting load carrying factor in a Kinematic system, the first thing that can be done is to dramatically increase the diameter of the spheres, (We have built precision spheres as large as eight inches [203 mm] in diameter, for Kinematic applications); but a system this large, or even larger, is gigantic and not very practical.

Use Stiffer Material

As an alternative to, or in addition to increasing the diameter of the sphere, the sphere can be made of a much stiffer material. There are several choices of material but the best one is, usually cemented Tungsten Carbide. It has a young's modulus of elasticity, or stiffness, of at least 98,000,000 PSI. This is over three times the stiffness of steel at 30,000,000 PSI. It is a very tough material when compared with other alternatives, such as sapphire or any of the ceramics.

It can be ground with a diamond wheel and diamond lapped to a very fine surface finish. It is electrically conductive, so that it can be machined, drilled and tapped using Electrical Discharge Machining. It is not an extremely expensive material.

Balls of this large size are usually custom designed and built to our customer's specifications.

Increase the Vee Block Angle

If changing the ball diameter and or material isn't enough, the design of the mating parts must be altered. The highest load carrying design uses three vee blocks and three mating spheres. The normal angle of the vee blocks is 90 degrees. By flattening this angle to 100 degrees a 20 percent increase in load carrying capacity can be achieved. A much lower resultant vector force causes this improvement. These vee blocks are custom designed to meet our customers mounting specifications.

The 100 degree included angle is just about the point of diminishing returns. When the angle gets much flatter than this, the repeatability of the Kinematic system decreases. Using this ploy, a system using three pieces of two and a quarter inch (57mm) diameter, tungsten carbide spheres and three, 100 degree vee blocks made of high chrome, high carbon, hardened stainless steel will safely carry 3300 pounds (1497 kg) of load. The five by seven foot (1.524m × 2.134m) system that used this design repeated to less than forty microinches (one micrometer).

The Canoe Sphere

The technique of using segments of a larger diameter sphere or of a large toroid has been used before (see addendum to our catalog 105B); but some recent work at M.I.T. by Dr. Alex Slocum and his students have come up with a very improved design, with huge load carrying capacity and excellent repeatability, yet in a very compact envelope. They call their design the "Canoe Sphere," based on its physical appearance. It is a compact monolithic design using two very large offset spherical radii. The break through innovation is that there are no loose pieces to be glued or screwed together.

We are producing an off the shelf version of the "Canoe Sphere" (our part number 2000-CS), that mates with our two inch vee block

Canoe Sphere Pricing

Part #	Description	Price
CS-1125-CPM	CANOE SPHERE, MINIATURE, 1.125"	$160.00
VB-2000-CPM	VEE BLOCK, 2" CYLINDRICAL POST MOUNTED	$173.00
VB-2000-SM	VEE BLOCK, 2" SURFACE MOUNTED	$173.00