Multibody Contact Modes - MapleSim Help

Multibody Contact Modes

 • Each force element in the Forces palette has a mode parameter that determines how the normal contact force is modeled.
 • There are three modes:
 – Linear spring and damper,
 – Linear spring and limited damper, and
 – Hunt and Crossley.
 • For each mode, the compression force, ${f}_{c}$, and damping force, ${f}_{d}$, are computed and then combined to arrive at the normal force, ${f}_{n}$. The compression force depends on the displacement, $u$, and the uncompressed length, ${L}_{0}$. The damping force depends on the velocity, $v$. The uncompressed length depends on the geometries of the contacting elements; for example, for two spheres it is the sum of their radii, while for a sphere and a disk it is the sum the radius of the sphere and the thickness of the disk.
 • If a contacting body penetrates more than half the uncompressed length, it penetrates the surface. To prevent penetration, the compression and damping factors should be increased.

Linear Spring and Damper

 • ${f}_{c}=\left\{\begin{array}{cc}-c\left(u-{L}_{0}\right)& u<{L}_{0}\\ 0& \mathrm{otherwise}\end{array}$
 • ${f}_{d}=\left\{\begin{array}{cc}-dv& u<{L}_{0}\\ 0& \mathrm{otherwise}\end{array}$
 • ${f}_{n}=\left\{\begin{array}{cc}{f}_{c}+{f}_{d}& {f}_{c}+{f}_{d}>0\\ 0& \mathrm{otherwise}\end{array}$
 • For a free body of mass $m$, the penetration depth with $d=0$ is $\sqrt{\frac{m}{c}}v$, and with $c=0$ is $\frac{m}{d}v$.

Linear Spring and Limited Damper

 • ${f}_{c}=\left\{\begin{array}{cc}-c\left(u-{L}_{0}\right)& u<{L}_{0}\\ 0& \mathrm{otherwise}\end{array}$
 • ${f}_{d}=\left\{\begin{array}{cc}-dv& u<{L}_{0}\\ 0& \mathrm{otherwise}\end{array}$
 • ${f}_{n}=\left\{\begin{array}{cc}{f}_{c}+\mathrm{min}\left({f}_{c},{f}_{d}\right)& {f}_{c}+{f}_{d}>0\\ 0& \mathrm{otherwise}\end{array}$

Hunt and Crossley

 • ${f}_{c}=\left\{\begin{array}{cc}-{c}_{n}{\left|u-{L}_{0}\right|}^{n}& u<{L}_{0}\\ 0& \mathrm{otherwise}\end{array}$
 • ${f}_{d}=\left\{\begin{array}{cc}-{d}_{n}v{\left|v\right|}^{q-1}{\left|u-{L}_{0}\right|}^{p}& u<{L}_{0}\\ 0& \mathrm{otherwise}\end{array}$
 • ${f}_{n}=\left\{\begin{array}{cc}{f}_{c}+{f}_{d}& {f}_{c}+{f}_{d}>0\\ 0& \mathrm{otherwise}\end{array}$