TwoGears1
2D

• TwoGears1[cnum, point1, rad1, point2, rad2, C] models a gear set. The rotational positions of the gears are related as per their respective radii.
• The constant C sets the initial rotational positions of the gears.
• TwoGears1 constrains one degree of freedom.

• The constant C, which sets the initial rotation of the gears, is given by the formula C = (rad1 e1 + rad2 e2) where e1 and e2 are determined in the following way. Place the two gears in any valid position and construct a vector from point1 to point2. e1 is the angle, measured in radians, from the constructed vector to the local x axis of gear 1 and e2 is the angle from the constructed vector to the x axis of gear 2.
• TwoGears1 is functionally identical to TwoGears2 except that the distance between the two gears is not constrained, only their angular orientation.
• If the Euler solution method is specified, TwoGears1 generates two constraints, and adds one extra variable to the model.
• TwoGears1[cnum, point1, rad1, {sym1, guess}, point2, rad2, 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.
• TwoGears1 is used primarily when other constraints are already constraining the location of the axes of the two gears so that TwoGears2 would be redundant.
• The first, and optional second, equation in TwoGears1 relates the rotation angles of the two gears.
• See also: RackAndPinion1, SetConstraints, SetSymbols, SysCon, TwoPulleys1.