TwoPulleys4
3D

• TwoPulleys4[cnum, axis1, rad1, {alpha, guess}, axis2, rad2, dist, C] is identical to TwoPulleys5 except that the heads of the two axes are not constrained to be adjacent. Thus, the two pulleys are free to slide on their axes, relative to each other.
• TwoPulleys4 constrains four degrees of freedom.

• TwoPulleys4 is essentially TwoPulleys5 with the third equation dropped.
• 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 pulleys, is given by the formula C = rad1 e1 - rad2 e2. e1 and e2 are determined in the following way. Place the two pulleys in any valid orientation 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 the angle from the vector to the reference direction of axis2.
• TwoPulleys4 generates five constraint equations and introduces one new variable, hence constraining four degrees of freedom.
• The first two equations in TwoPulleys5 constrain axis1 to be parallel to axis2, the third equation constrains the axes to be dist units apart, and the fourth and fifth equations relate the value of the variable alpha to the rotational displacements of the pulleys.
• See also: ParallelGears4, SetConstraints, SetSymbols, SysCon.