Machine Design

These mounts don't get the "point"

Replacing point contacts with line contacts boosts load capacity of kinematic mounts.

Senior Editor

Spherolinder connectors come in stainless steel, tungsten carbide, hightemperature ceramics, and engineering plastics. Applications include precisionaligned components such as silicon-chip inspection equipment, airborne targeting systems and rocket motors, and optical instruments with large lens assemblies that are sensitive to warping when secured.

Repeatable kinematic mounts locate two parts in relation to one other, quickly and with submicron precision, making them ideal for delicate equipment and processes that need frequent assembly and disassembly. Conventional kinematic mounts separate parts with three precision-ground spheres. Spheres are located by machined grooves spaced 120° apart on one part surface, and by cone-shaped holes on the other. The arrangement effectively eliminates movement in all six degrees of freedom, without clamps and overconstraint that may warp or distort parts. Instead, a single bolt passed through the center of each sphere is sufficient to fix the parts. However, heavy loads and impact shocks can easily damage the spheres because of high-stress point contacts between them and the V-grooves.

But concentric half-sphere/ halfcylinders (Spherolinders) from G2 Engineering, Mountain View, Calif., eliminate single-point contacts and replace them with line contacts, without loss of positioning integrity. Calculations and tests show the mounting scheme can significantly boost load capacity. For example, assuming an evenly distributed load, a conventional mount with three 440C stainless-steel spherical connectors of 1-in. diameter handles loads to 440 lb. A mount fitted with Spherolinders of the same size and material supports-33,000 lb. Regardless of the type of connector used, kinematic mounts share common shortcomings that can limit repeatability. One issue is preseating. Mediating connectors (spheres or Spherolinders) are assumed to self-locate to their nominal positions under simple friction force. But for micron-level motions, Hertzian contact stresses dominate. In other words, local elastic deformations are on the same order of magnitude, or larger than, relative motion of the parts.

Trapped particulates are another concern because they can trigger misalignment and damage mating surfaces. Spherolinders have much smaller radii of curvature than spheres of equal load capacity and therefore present less nonmating surface area for contaminants to cling to. Still, as with any precision assembly, air free of damaging particulates is key to proper operation.

Surface-contamination layers, on the other hand, tend not to damage mating surfaces and may, in fact, help with lubrication. The problem here is what is called "slow creep." A greasy layer can let mating connectors "float" initially, then slowly sink together with time, depending on load and radius of curvature. The smaller radius of curvature afforded by the Spherolinder mitigates these effects.

Kinematic mounts, by design, permit loose tolerances on mating bodies, though the mating features themselves are held to tight tolerances, including the surface finish. Spherolinders are more geometrically complex than spheres, so there are more tolerances to watch. A small amount of angular motion allowed by the retaining bolt mitigates minor eccentricities. Small deviations in cylindricity and sphericity are averaged out in the line contacts, all within the bounds of elastic deformations.

Kinematic Mounts By The Numbers

Sphere-to-groove point contacts are what limit load capacity in conventional sphere-based kinematic mounts. Those with a V-groove full angle of 120° handle more load than with 90°, but at the expense of weaker centering forces. Spherolinders replace the point contacts with line contacts. Maximum allowed forces at the contact interfaces are:

The top, spherical portion of a Spherolinder touches a cone about a circumference. The bottom, cylindrical portion has two line contacts whose total length equals twice the cylinder length.

The length of a cone-sphere contact line is:

The optimal length to match load capacity of both the top and bottom Spherolinder surfaces (assuming a 90° cone) is:

The above calculations are for a single mounting site. A complete mount contains three mounting sites so load is adjusted accordingly.

G2 Engineering

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