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The following excerpt is from the Revised Manual of Gear Design, Section III, covering helical and spiral gears. This section on helical gear mathematics shows the detailed solutions to many general helical gearing problems. In each case, a definite example has been worked out to illustrate the solution. All equations are arranged in their most effective form for use on a computer or calculating machine.
In our last issue, the labels on the drawings illustrating "Involutometry" by Harlan Van Gerpan and C. Kent Reece were inadvertently omitted. For your convenience we have reproduced the corrected illustrations here. We regret any inconvenience this may have caused our readers.
Involute Curve Fundamentals. Over the years many different curves have been considered for the profile of a gear tooth. Today nearly every gear tooth uses as involute profile. The involute curve may be described as the curve generated by the end of a string that is unwrapped from a cylinder. (See Fig. 1) The circumference of the cylinder is called the base circle.
Among the various types of gearing systems available to the gear application engineer is the versatile and unique worm and worm gear set. In the simpler form of a cylindrical worm meshing at 90 degree axis angle with an enveloping worm gear, it is widely used and has become a traditional form of gearing. (See Fig. 1) This is evidenced by the large number of gear shops specializing in or supplying such gear sets in unassembled form or as complete gear boxes. Special designs as well as standardized ratio sets covering wide ratio ranges and center distanced are available with many as stock catalog products.
These lines, interesting enough, are from the notebooks of an artist whose images are part of the basic iconography of Western culture. Even people who have never set foot in a museum and wouldn't know a painting by Corregio from a sculpture by Calder, recognize the Mona Lisa. But Leonardo da Vinci was much more than an artist. He was also a man of science who worked in anatomy, botany, cartography, geology, mathematics, aeronautics, optics, mechanics, astronomy, hydraulics, sonics, civil engineering, weaponry and city planning. There was little in nature that did not interest Leonardo enough to at least make a sketch of it. Much of it became a matter of lifelong study. The breadth of his interests, knowledge, foresight, innovation and imagination is difficult to grasp.
For years, politicians, educators and business leaders have generated various ideas to revitalize U.S. manufacturing and engineering. These include manufacturing initiatives, internal training programs and an emphasis on science, technology, engineering and mathematics (STEM) in the classroom. The declining expertise in these fields, however, continues to be a growing problem in every facet of manufacturing and engineering.