Established in 1952323.582.7348800.322.5832 Page: 4890Friday, December 13, 2013

# Large Kinematic Structures

We will qualify a large kinematic structure as one covering an area measured in square yards, (meters) rather than square inches, (centimeters).

There are basically two dilemmas influencing the use of kinematic support for large payloads. Large structures are heavy and large structures are flexible. The flexibility is due to stresses imparted to the structure by its own mass and the mass of the payload.

#### Canoe Sphere

If the flexing associated with only three points of support can be tolerated, then the three canoe spheres and three vee-blocks are a very simple and a very accurate answer. A canoe sphere consists of two symmetrical segments of a forty inch (one meter) diameter sphere, that is precision ground in a compact monolithical form.)

Each combination of Canoe Sphere and Vee-block will support a 5000 pound ( 2268 kg ) load. This amounts to a maximum 15,000 pound ( 6804 kg) total load carrying capacity, for a full complement of kinematic components.

#### Whiffletree

In situations where the elastic sag associated with only three points of contact cannot be tolerated, a unique approach called the whiffletree can be used.

If we rationalize the basic rule of kinematic couplings which states, that “you should use the fewest points of contact needed to constrain the degrees of freedom necessary,” to a new statement that you should use the fewest points of contact that will limit the flexural deflection of a given area of the structure to an acceptable limit, we can then support large structures by truly kinematic means. If this rationalization doesn’t sit well, we can just call this approach “Semi Kinematic” or “Pseudo Kinematic” and get on with it.

Kinematic couplings are usually very limited in load carrying capacity, but by using the multi contact approach of the whiffletree that, provides so many additional kinematic couples in a given system, this limitation can be minimized.

The approach we will use, is many centuries old in the west, and many thousands of years old in China. The current terminology for this technology is the “Whiffletree”.

The simplest version of the Whiffletree is a single balancing beam with the load at the center and the load carrying, or load supporting force, applied to each end. With this simple arrangement the load is equally divided by two. By adding another balancing beam at each end of the original beam, we now equally divide the load by four. By adding still another balancing beam at the ends of these beams we equally divide the load by eight.

#### Trivet

By placing a three spoked Trivet on the ends of the last two balancing beams instead of a simple beam, we now equally divide the load by twelve.

By placing a true kinematic couple at each of the pivot points, extremely accurate support of a large, heavy distributed load may be achieved.

Using the principal of reversibility, we can use the same concept to spread out the load over a large number of supporting points and concentrate it in a limited number of places of support. Going another step further, we can provide multiple Whiffletrees in sets of three that will all be self balancing.

The whiffletree is such a universal concept that varieties of it are only limited by the designers' imagination.

#### Kelvin Trihedral Couple

A powerful form of kinematic couple that constrains three degrees of freedom, is the Kelvin trihedral clamp and a mating sphere.

A less complicated and less expensive approach is to use a conical cup with three undercuts that leave three load carrying lands. However, this approach is much less accurate.

By dividing the load into multiple points, we end up multiplying the load on the final supporting mechanisms.

In the final few supporting devices, it may be required that we use coupling that are somewhat less than kinematic in order to adequately support these heavy loads.

#### Clevis

One widely used device having a single degree of freedom is the clevis. It offers one degree of rotary freedom with very high load carrying capacity.

This device consists of a U shaped shackle, that encompasses a tongue, with a cylindrical pin (called a clevis pin) connecting them together.

By using a precision ground shoulder bolt as the clevis pin and precision reamed holes in the clevis and the tongue, fairly precise alignment can be maintained.

#### Spherical Cup

Another popular approach for the heavy load carrying devices is the spherical cup, or a conical cup with a very precise spherical annulus lapped in it. These devices are subject to stick and slip problems but they do offer very high load carrying capacity and complete freedom of alignment in pitch, yaw and roll. This spherical bearing has a large area of contact which allows the use of a lubricant.

In analyzing the Whiffletree approach for supporting large loads, it should be realized that this device acts like a long lever. Large excursions of the load reflect as only very short excursions at the central load bearing element, so that self alignment is far less critical than might be expected.

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