# Define Preload, Offset and Scale

^{th}direction (x, y, z, ax, ay, az) is defined by a function:

- ${F}_{k}$
- Force in the k
^{th}direction - ${G}_{k}({d}_{k},{\dot{d}}_{k},{x}_{k},t)$
- Force function in the k
^{th}direction - ${d}_{k}$
- Displacement input in the k
^{th}direction - ${\dot{d}}_{k}$
- Velocity input in the k
^{th}direction - ${x}_{k}$
- Array of internal state (that is, hysteresis) in the k
^{th}direction - $t$
- Time

The displacement offset Q_{k} and the displacement scale
H_{k} modify the displacement and velocity to compute new inputs to
function G as follows:

${q}_{k}={H}_{k}\cdot {d}_{k}-{Q}_{k}$ is the scaled, offset displacement.

${\dot{q}}_{k}={H}_{k}\cdot {d}_{k}$ is the scaled velocity.

_{k}and force/torque scale V

_{k}modify the output so the force computation is: