It is sometimes necessary that the reciprocating rectilinear motion shall be performed at a certain varying rate in both directions. This may be accomplished by the machine represented in _fig. 162._ A wheel upon the axle C turns uniformly in the direction A B D E. A rod _mn_ moves in guides, which only permit it to ascend and descend perpendicularly. Its extremity _m_ rests upon a path or groove raised from the face of the wheel, and shaped into such a curve that as the wheel revolves the rod _mn_ shall be moved alternately in opposite directions through the guides, with the required velocity. The manner in which the velocity varies will depend on the form given to the groove or channel raised upon the face of the wheel, and this may be shaped so as to give any variation to the motion of the rod _mn_ which may be required for the purpose to which it is to be applied. The _rose-engine_ in the turning-lathe is constructed on this principle. It is also used in spinning machinery. It is often necessary that the rod to which reciprocating motion is communicated shall be urged by the same force in both directions. A wheel partially furnished with teeth, acting on two racks placed on different sides of it, and both connected with the bar or rod to which the reciprocating motion is to be communicated, will accomplish this. Such an apparatus is represented in _fig. 163._, and needs no further explanation. Another contrivance for the same purpose is shown in _fig. 164._, where A is a wheel turned by a winch H, and connected with a rod or beam moving in guides by the joint _ab_. As the wheel A is turned by the winch H the beam is moved between the guides alternately in opposite directions, the extent of its range being governed by the length of the diameter of the wheel. Such an apparatus is used for grinding and polishing plane surfaces, and also occurs in silk machinery. An apparatus applied by M. Zureda in a machine for pricking holes in leather is represented in _fig. 165._ The wheel A B has its circumference formed into teeth, the shape of which may be varied according to the circumstances under which it is to be applied. One extremity of the rod _ab_ rests upon the teeth of the wheel upon which it is pressed by a spring at the other extremity. When the wheel revolves, it communicates to this rod a reciprocating rectilinear motion.