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OrthogonalGears5
3D

OrthogonalGears5[cnum, axis1, teeth1, {alpha, guess}, axis2, teeth2, C] models a pair of gears on orthogonal axes, such as a bevel gear set.
• The axes of the two gears, axis1 and axis2, are constrained to be orthogonal, and the origins of these two axes are constrained to be coincident. The rotational positions of the two gears are related as per their respective tooth counts, teeth1 and teeth2.
• Negating teeth1 or teeth2 reverses the relative direction of rotation of the gears.
OrthogonalGears5 constrains five degrees of freedom.

OrthogonalGears5[cnum, axis1, teeth1, {alpha, guess}, axis2, teeth2, dist, C] offsets the axes of the gears by dist units, such as the offset in a worm gear or spiral bevel gear set.
• The symbol alpha tracks the relative spin of axis1.
• The constant C, which sets the initial positions of the two gears, is given by the formula C = teeth1 e1 + teeth2 e2. e1 and e2 are determined in the following way. Place the two gears in any valid position. e1 is the projected angle, in radians, measured from axis2 to the reference direction of axis1, and e2 is the angle from axis1 to the reference direction of axis2.
OrthogonalGears5 generates six constraint equations and introduces one new variable, hence constraining five degrees of freedom.
• The first equation in OrthogonalGears5 constrains axis1 to be orthogonal to axis2, the next two equations constrain the origins of the two axes to be adjacent, the fourth equation constrains the axes to be dist units apart, and the fifth and sixth equations relate the value of the variable alpha to the relative rotation of the two gears.
• See also:
ConstantVelocity4, Orthogonal1, ParallelGears5, SetConstraints, SetSymbols, SysCon.


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