## Manufacturing

Problems and tasks from a variety of sources intended to illustrate the way mathematics arises in life and work.

Drilling Holes. A machinist must drill five 1/4 inch holes equally spaced on a circle with a 2.9" radius. Find the coordinates of the centers of these holes.

Sine Table. Explain how to set up a sine table as a jig for a drilling machine in order to properly drill a hole at a precise angle. (A sine table is a platform with hinges on two sides that permit tilting along two horizontal axes.)

Mating a Part. Given a machined part, calipers, micrometers, and depth gauges, prepare a scale drawing of a second mating part within a tolerance of .030".

Gear Trains. In typical gear boxes, four gears (A,B,C,D) with teeth (a,b,c,d) are arranged so that A drives C which is keyed to B, which drives D. Thus the ratio of driver to driven is ab/cd. If a ratio r is desired, one seeks values of a,b,c,d in the range of 20 to 100 (practical limits for the number of teeth) to makes ab/cd as close as possible to r.

Glass Production. A report from a manufacturing plant describes the process of making glass, which after leaving the mixing vat flows down the production line like an incandescent river, giving rise to a variety of questions about tons per day of production, the line speed, and the glass river's width and thickness. Because the glass must be cut into sections as it is moving along the production line, the glass cutters must be positioned at precise angles so that when the cut is complete the glass will be sectioned into rectangles.