computing a wheel trajectory

Hello, I have a simple device : a vertical wheel bound to an horizontal bar. The bar always belongs to the plan of the wheel (the wheel is bounded
to follow the bar direction). The movement of the wheel is intended to perform without slipping. Which is the path taken by the wheel when one pulls or push the bar from the opposite end constrained to follow an arbitrary trajectory ? I can solve the problem when the trajectory is a line with a non trivial initial condition corresponding to a wheel contact point not being in line whith the linear trajectory (a solution of the differential equation y'(x)^ 2 + 1 - 1/x^2 = 0). What approach do you suggest for the general case ? Thank you for your help. Claude Animo
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