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Derpson
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In 2D machines, why does higher pair joints deduct 1 D.O.F.?

I have been taught that higher pair joints (e.g. Gears, cams, rollers) deduct 1 d.o.f. Due to the fact that they still allow 2 motions 1.) translation along the tangent surface 2.) rotation around the instantaneous Contact point

However, from my reasonings, the higher pair does constrain 2 motions 1.) as it is non-slipping (like gears and rollers) it gives a relationship between the angle and the location (such as x=theta * r) 2.) as it rotates on a surface it gives a relationship between x and y that it household be on the surface (such as x = y+2)

Thank you for your answers

Derpson
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