RackAndPinion5
3D• RackAndPinion5[cnum, axis1, rad, {alpha, guess}, axis2, C] models a rack and pinion gear set. axis1 represents the rotational axis of the pinion, and axis2 represents the rack. axis2 is parallel to the cut of the teeth of the rack, and axis2 and its reference direction lie in the plane of the rack. axis1 is constrained to lie rad units away from, and parallel to, axis2, and the origins of the two axes are constrained to be adjacent. The rotational orientation of the pinion is related to that of the rack as per the pinion radius.
• RackAndPinion5 constrains five degrees of freedom. • The symbol alpha is used as the pinion rotation variable.
• RackAndPinion5 generates six constraint equations and introduces one new variable, hence constraining five degrees of freedom.
• The two equations in RackAndPinion5 constrain axis2 to be parallel to axis1, the third equation places the pinion axis rad units away from the rack, the fourth equation constrains the origin of the pinion to be adjacent to the origin of the rack, the fifth equation relates the axial displacement of the rack to the rotation of the pinion, and the sixth relates the value of the variable alpha to the rotation of the pinion.
• See also: Cylindrical4, LeadScrew5, RackAndPinion4, ParallelGears5, SetConstraints, SetSymbols, SysCon.
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