Dissipation Factor - Path Spring

[Pia Stefanek]

Hi,

Unfortunately I could not find a definition for the dissipation factor (s/m), which is a parameter of the path spring class. Is it correct when I say that the dissipation factor defines the recoil time for the spring per meter?

Thank you
Pia

[Thomas Uchida]

Please see the doxygen documentation for the PathSpring class (https://simtk.org/api_docs/opensim/api_ ... ml#details): "The tension is proportional to its stretch beyond its resting length and the amount of dissipation scales with amount of stretch, such that tension = (K*s)*(1+D*ldot) where stretch, s = l-lo for l > lo, and 0 otherwise. l is the path length of the spring and lo is its rest length. K is the linear stiffness and D is the dissipation factor. When l < lo the spring applies no tension to the bodies and considered to be slack."

[Pia Stefanek]

Thank you for your Reply.

I read the doxygen documentation for the PathSpring class. But I only know that the Dissipation factor is D. But how is the factor defined?

[Thomas Uchida]

how is the factor defined?

As shown in the equation above, D describes how tension is affected by the rate of stretch.

[Pia Stefanek]

So it is just a parameter that links tension to stretch. Is this correct?
One cannot say that is has something to do with the recoil time of the spring?

Excuse me for asking so much I just want to be sure.
Thank you very much.

[Thomas Uchida]

Excuse me for asking so much I just want to be sure.

I recommend running some simple simulations (e.g., adapting the OpenSim tug-of-war example to use a single PathSpring, or writing a short MATLAB program) to gain insight into the time response of the system for different values of these parameters.

[Pia Stefanek]

Hm I tried some simulations but it is not so easy to understand.
Only when T=K*s -> D=-1/v. Only when T=Ks, the spring is linear and dissipation expresses the recoil time for the spring per meter.

[Thomas Uchida]

Only when T=K*s -> D=-1/v. Only when T=Ks, the spring is linear and dissipation expresses the recoil time for the spring per meter.

Perhaps it would be more helpful to think of D in terms of (1 / (m/s)): a multiplicative factor describing the force contribution arising from 1 m/s of stretch rate. In general, increasing D will make the system more "sluggish"; quantifying that will depend on how you define "recoil time" for this nonlinear spring. Expanding the equation given in the documentation:
tension = -K Lo + K L(t) - K D Lo Ldot(t) + K D L(t) Ldot(t)
where the length L(t) and stretch rate Ldot(t) of the spring are functions of time. If necessary, you could try linearizing this equation around an operating point to analyze more deeply.