• ParallelGears5[cnum, axis1, rad1, {alpha, guess}, axis2, rad2, C] models a gear set.• The axes of the two gears, axis1 and axis2 are constrained to be parallel and rad1+rad2 units apart, and the heads of the two axes are constrained to be adjacent. The rotational positions of the gears are related as per their respective radii.• ParallelGears5 constrains five degrees of freedom.

• The symbol alpha tracks the spin of axis1, relative to a vector spanning from axis1 to axis2.• The constant C, which sets the initial positions of the gears, is given by the formula C = rad1 e1 + rad2 e2. e1 and e2 are determined in the following way. Place the two gears in any valid position and construct a vector from the origin of axis1 to that of axis2. e1 is the angle, in radians, measured from the constructed vector to the reference direction of axis1, and e2 is measured from the vector to the reference direction of axis2.• ParallelGears5 generates six constraint equations and introduces one new variable, hence constraining five degrees of freedom.• The first two equations in ParallelGears5 constrain axis1 to be parallel to axis2, the third equation constrains the origin of axis2 to lie adjacent to axis1, the fourth equation constrains the axes to be rad1+rad2 units apart, and the fifth and sixth equations relate the value of the variable alpha to the rotational displacements of the gears.• See also: OrthogonalGears5, Parallel2, SetConstraints, SetSymbols, SysCon.