Invented by Girolamo Cardano in the 16th century the Cardan gear is a way of converting rotary motion into straight line motion. Watch how the red dot on the inner purple gear exactly follows the vertical dotted line. The outer gear has a diameter exactly twice as large as the inner gear. In the above example they have 40 and 20 teeth respectively. Cardano also invented a type of universal joint and investigated the mathematics of probability. Understanding the mathematics of risk helped him make a living from gambling until eventually he could find no-one to gamble with and had to move onto new pastures...
Rack and Pinion
The rack and pinion is used to convert between rotary and linear motion. The rack is the flat, toothed part, the pinion is the gear. Rack and pinion can convert from rotary to linear of from linear to rotary.
On the left is a simple pulley. As the rope is pulled down the weight moves up by the same distance. In the compound pulley on the right the rope is wrapped around two pulleys. As the rope is pulled the weight, this time attached to the lower pulley rather than direct to the rope, moves up slower than the speed that the rope is pulled. Corresponding to this reduction in speed is an increase in the force on the weight. The amount of increase in the force depends on how many times the rope wraps round the pulleys. By wrapping the rope several times around the pulleys it is easily possible to lift your own weight off the ground!
Belt drives are used transfer rotational motion from one place to another.
On the left, both pulleys are the same size. Drive can be transfered by friction of the belt on the pulley or, if required, buy using a toothed belt. Chain drives work in a similar way. By crossing the belt the direction of drive can be changed. On the right two sizes of pulley are used to show how speed of rotation can be changed.
This mechanism is used to convert between rotary motion and reciprocating motion, it works either way. Notice how the speed of the piston changes. The piston starts from one end, and increases its speed. It reaches maximum speed in the middle of its travel then gradually slows down until it reaches the end of its travel.
The bell crank is used to convert the direction of reciprocating movement. By varying the angle of the crank piece it can be used to change the angle of movement from 1 degree to 180 degrees. The bell crank was originally used in large house to operate the servant’s bell, hence the name.
“Jeeves, where’s my tea?!”
Download and make your own bell crank mechanism here.
There's an updated animation here: