# RackAndPinion12D

RackAndPinion1[cnum, point, rad, axis, C] models a rack and pinion gear set where axis represents the rack and point is the center of the pinion. The angular orientation of the rack and pinion are related as per the pinion radius rad and the displacement between the origin of axis and point, measured in the direction of axis.
• The constant C sets the initial orientation of the rack and pinion.
RackAndPinion1 constrains one degree of freedom.

• The constant C is the distance, in the direction of axis, from the origin of axis to point when the x axis of the pinion body is parallel to the rack.
RackAndPinion1 is functionally identical to
RackAndPinion2 except that the distance between the rack and the pinion is not constrained, only their angular orientation.
• If the Euler solution method is specified, RackAndPinion1 generates two constraints, and adds one extra variable to the model. RackAndPinion1[cnum, point, rad, {alpha, guess}, axis, C] can be used to explicitly specify the name of the extra variable alpha, and its initial guess. Otherwise, a symbol of the form cnum is used.
RackAndPinion1[cnum, point, rad, {sym1, guess}, axis, C] can be used to explicitly specify the name of the extra variable and its initial guess. Otherwise, a symbol of the form cnum is used.
• The first, and optional second, equations in RackAndPinion1 relate the relative displacement of the rack and pinion to their relative rotation.