This is a museum display. It's showing a skidoo brand snowmobile's rear suspension. I think it's supposed to show off the large travel distance
for this particular model, the R-Motion.
That would explain the numbers printed on the right side of the case
Reading from a 2011 article about this on snowmobile.com It says: "the new suspension, named rMotion, will offer the greatest rising-rate motion-ratio of any existing rear suspension"
whatever that means
"the new suspension combines a rising rate with all new degrees of adjustability that give this design an increased “sweet spot”"
Ok!
"The design goal was to maintain comfort and control in the small chatter bumps while adding capability in deeper moguls"
Of course.
This museum is right near the factory where they actually make these.
The company is called BRP and it stands for Bombardier Recreational Products. They make Snowmobiles and Jet skis among other things
You might have heard of SKI DOO and SEA DOO ?