Re: [CAD_CAM_EDM_DRO] Hexapod question - rigidity

Simon,

Thanks for the pictures off list. Now I think I see the problem.

Although legs don't have to make triangles, the arrangement you have can
not be rigid. Having the legs equally spaced for both the base and
platform creates the situation where the platform position can change
without a change in leg lengths.

For example, consider the case where the legs are all equal length.

The platform will hang below the base, at a particular Z position. It is
not a unique solution to the kinematics, however. If the platform were to
be rotated about the Z-axis, the legs could still have the same lengths,
but the platform would rise toward the base along the Z-axis.

For a particular leg length, the platform can rotate about the Z-axis,
while simultaneously moving along the Z-axis.

In practice, your legs probably aren't *exactly* evenly spaced along both
the base and the platform, and the inexactness will give you some
rigidity. You may also have friction in your joints, which will resist
moving the platform.

The simplest change that would (IMO) give you more rigidity would be to
mount the base joints as close together as you can, in pairs. Then, a
change the platform position would not be possible without a change in at
least one leg length.

In math terms. the solutions to the forward kinematics equation must be
points in 6-space (X, Y, Z, Pitch, Roll, and yaW). The situation you have
now looks like it creates solutions which are
lines in 6-space, and you can move freely anywhere along the line.

-- Carl