# Mass on a plane, 'sideways' force on three points

I am trying to model sideways forces on three hydraulic cylinders (or 'legs) of different lengths resting on tilted ground, connected to a solid rectangular chassis with a center of mass slightly elevated above the plane of said chassis.

In my model I have a 'ground plane' that has a fixed pitch and roll, with the plane of the chassis elevated above that standing on the three legs. Each leg is connected to the chassis plane at a fixed (x,y) coordinate, and extends by length (l) perpendicular to the chassis plane to touch the ground plane. The center of mass above the chassis plane, when projected downward (in the direction of gravity) on to the chassis plane, is always inside the triangle formed by the three connection points.

I'm interested in the sideways force on the legs because in certain configurations, a cylinder can 'jam' and I'm assuming this is due to friction between the shaft and it's socket.

To complicate things slightly, and perhaps unnecessarily, there is an additional stress on the cylinder caused by friction of the foot pad with the ground, caused by any change in the length of any cylinder after they have been 'planted'. In the real world, the chassis is mounted on tracks which hold the weight until the jacks touch the ground (it's a blast-hole drill rig).

Any ideas? My trig-force-vector-foo is failing me. To begin with I'd just like to know how to distribute weight to the three points on the chassis plane.

Excuse my dodgy gimp skills, but here's an attempt to illustrate the model:

Given the ground pitch and roll, and the length of each leg, I can relatively easily determine the pitch and roll of the chassis plane. The height of the COM above the chassis can be taken out by projecting it downward onto the chassis plane. Once I know the downward force on the point where each cylinder attaches to the chassis, I can decompose that into the forces along the cylinder and across it.

This google image search shows the kind of vehicle I'm looking at.

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Would you be able to post a diagram of this? –  Mike Jul 3 '13 at 2:22