By Brian Bolt
A source booklet which seems on the layout of mechanisms, for instance gears and linkages, in the course of the eyes of a mathematician. There are a large choice of examples together with motor vehicle guidance, anglepoise lamps, bicycles, cine cameras, folding push chairs and the layout of robots. Readers are inspired to make versions all through and to appear for additional examples in way of life. compatible for GCSE, a degree, and mathematics/technology/engineering classes in extra schooling.
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Extra info for Mathematics Meets Technology
6 A mechanism is made from two strips AC and BD as shown below, such that AC=BC. Fix A by using a drawing pin into a drawing board, or paper fastener into a large piece of card or paper. Draw a straight line across the paper through A and then trace the locus of different points P of DB as B moves along the line. Why is the locus of C a circle? pencil A B Allow C to make a complete circle about A while keeping B on the line, to obtain the true paths of points like P. 46 7 An ironing board is to be made to be adjustable with working heights of 60 cm, 65 cm, 70 cm, 75 cm, and 80 cm.
In many situations spur gears are used to reduce the speed of rotation of the output shaft compared to the driver. This is the case with a winch or electric drill or a food mixer. It is achieved by having spur wheels with a small number of teeth driving spur wheels with a large number of teeth. The gear train below is for a winch. The follower, which is driver follower connected directly to a winding drum, will turn at ^ of the speed of the driver, so that a person turning a handle to operate A will gain a considerable mechanical advantage.
Exercise 3 1 Make a variable-based triangle using a construction kit or cardboard strips and paper fasteners. Change x the length of AB and measure the value of 0 for each value of x you use. Plot a graph of 6 against x o o o o o o o o o o o o o q j ) B mmmmmmmmmmmm—mm X Cm • M M M M M H M ^ What is (i) the smallest value of 0, (ii) the largest value of 0? Does 0 change in equal amounts for equal changes in xl 45 2 A variable-based triangle has A C=8 cm, CB=6 cm and AB can take values of 3 cm, 4 cm, 5 cm, 6 cm, 7 cm, 8 cm, 9 cm, 10 cm.