Designing Gears Through the Years

A glance back to the early days of gear design will give you a newfound appreciation for the equipment and technology that speeds your progress through an average workday.


In the past 50 years, we’ve certainly come a long way in terms of our gear design and problem-solving capabilities. But even though the analog world was considerably different from the digital world we find ourselves in today, many of the problems were not so different. So how were problems related to gears solved back in the old days?

To begin with, it must be said that the tools available then were completely different from what is utilized today. These days solutions revolve around computers and the software that is available to meet gearing challenges. The list seems endless, and the choices are sometimes difficult to make when choosing the “right” software that moves one quickly toward a solution.

To discuss gear design prior to these innovations, it’s necessary to go “back to the drawing board,” as we used to say… make that drawing boards, T-squares, triangles, and even drafting machines of various configurations. This drafting equipment came in a variety of sizes, and some were quite large since it was useful to do preliminary design in the part’s actual size. Keeping a sense of size proportion while working on a computer monitor can be more difficult because of the limitations imposed by screen size. For durability, some drawings were made on linen using India ink, which was especially dark and long-lasting. Drawing instruments were required as well, including compasses, dividers, and ink pens. These were precision instruments, and at the beginning of World War II a crisis developed since most of these instruments were imported from Europe–especially Germany–and therefore became hard to obtain. An innovative American company was given the task of eliminating this shortage and developed a unique set of precision instruments using laminated steel that didn’t require highly skilled handwork to manufacture.

The most indispensable tool was the slide rule. In the hands of an expert one could “see” the relationships that were being analyzed or calculated in an almost dynamic fashion. A series of parameters could be “seen” to optimize themselves on the slide rule. A slide rule was usually six to 12 inches long, but could be twice that length or more. Twelve inches seemed to be the most popular length. Some were circular, and they came in many sizes as well. A popular size was one that fit into a shirt pocket, much like the PDAs of today. Other advantages were that many different kinds of calculations could be done on the same slide rule, and it was compact, lightweight, and didn’t need batteries. The disadvantages were that accuracy was not to be successfully pushed beyond three significant figures, and the decimal point location was always kept in your head. Since you had to keep track of the decimal point, you always had a sense of the magnitude of the answer as well as the perspective of the problem. Since gearing required such a high degree of accuracy, the slide rule was most often used in preliminary gear design, especially when designing the gearing components used in various kinds of transmissions, including shafts, bearings, and keys.

Other tools that were used extensively were alignment charts and special slide rules. Alignment charts were constructed for a specific equation that was needed for highly repetitive calculation. The chart usually consisted of a series of scaled parameters positioned in such a way as to allow you to lay a ruler across the scales, with one of the scales providing the answer. It functioned much like some of the software programs we have today. Special slide rules were similar, except that you could align the scales to obtain the result.

So how did we go about achieving the required accuracy? By using huge, bulky books of 10- to 12-place log tables, trig tables, and involute tables. One of the gear engineer’s most valuable possessions was a copy of Werner Vogel’s book, Involutometry & Trigonometry. The tables in this book provided the values needed in the accurate specification of gearing parameters. It was slow and tedious work, not only to come up with the specific dimensions and tolerances, but also to select the “change gears” for the mechanical gear machinery of the day. The selection of a train of change gears to cut a specific geared part was an exercise made easier by the length of one’s experience in the selection process. This calculation was also simplified if the geared part relationship involved integers. In worm gear design, you always wanted an axial pitch that was divisible by a whole number without a remainder.

When a gear housing required a center distance at an angle to a base reference, it was necessary to use Pythagorean relationships. This was because many machine tools of the day were restricted to only “X” and “Y” movements. One needed to calculate the X and Y dimensions with tolerances so that the center distance tolerance specification was maintained. More hard, tedious work ensued. I know of an engineer who taught himself how to use an abacus, because that allowed him to do squares of numbers and square roots without the use of log tables. A mathematical continuous series could also be used, with calculations ending when the series yielded the precision required.

Component design in geared transmissions was aided by many bearing and steel companies. These vendors provided all the information needed in a published format. One bearing vendor supplied to scale bearing outline templates that could be quickly traced onto a drawing, much like downloading templates into today’s computer design programs.

In preliminary design, iteration was limited. Specific points could be calculated from known design functions, however, and plotted on graph paper. The engineer would then study the relationships and inflections of the plotted information to optimize the design. One of the great advantages of today’s design software is that it provides a consistency of design regardless of the engineer working on the problem. This was accomplished by elaborate procedural design sheets to be filled in by the design engineer, the drafter, or the manufacturing engineer. This would then become part of the official paper trail. Today we have many technologies that enable rapid prototyping, and an earlier form of this existed as well. Depending on the need, gear transmission gear cases and housings could be obtained in wood or cast iron. Doesn’t sound too fast, does it? Well, there were many skilled pattern makers who could work from sketches to craft the needed patterns and resulting parts quickly. What really made the process move along was that many of the larger companies had their own in-house pattern shop and dedicated prototype machine shop. The engineer worked right alongside the pattern maker to resolve any issues as they arose.

The resulting prototypes served numerous purposes, even beyond the more obvious matters of fit, form, and performance. Using two-dimensional drawings required the engineer to make sure that the internal clearances of rotating components were correct and that there were no drawing errors. Also important were the thermal considerations needed in the design of a family of geared products.

It was necessary to run performance tests as quickly as possible to verify that the design of the geared enclosures had the required thermal dissipating characteristics. This was usually accomplished by beginning the design of the smaller units, which were not expected to have thermal issues, and then proceed to the larger sizes. From the test data one could then extrapolate the needed surface area for the next larger size to insure that the necessary surface area would be present, and thus have the correct heat dissipating characteristics. Sounds straightforward enough, but the problem was how to accurately determine the surface. And you didn’t have a computer-designed solid model to rely on back then.

Surface area calculations for the more simple housing components were completed using the two-dimensional drawings, but many were more complex, and simple calculations did not suffice. So here is a method for solving that problem: Using very thin tinfoil, one would carefully apply the foil to the part. It required a steady hand to apply the foil and not to crinkle or overlap it in any way–it had to be a single, second skin over the part. Depending on part size, this could be a two- or three-day process. Then, when the process was completed and it was really looking good, the next step was taken. If this process was done by a person for the first time, then their mentor might appear, seeming to admire the work, but suddenly removing all of the foil with no regard for the care with which it had been applied. Having removed all of the foil it was usually formed into a nice ball, much to the chagrin of the person who applied the second skin. The ball of foil was then weighed and the surface area determined. A known square piece of the foil had previously been weighed, and the volume of this known piece was the result of its length, width, and thickness. Since the thickness was very small compared to the length and width, it was ignored. Therefore, the surface area of the known sample was directly proportional to its weight. The weight of the ball of foil from the part gave the surface area.

Performance of a geared product has always been important. In a right angle geared unit it is crucial to know the efficiency. The input load was determined by using an electric motor that was itself calibrated as to input and output power. This would be connected to a reducer. On the output side of the reducer a pulley was assembled, and this would be suspended overhead with a “spring scale” attached to a rope. The rope would be carefully wrapped around the pulley and the drive started. The wrapped pulley would need to be carefully held by hand to guard against slipping between the rope and the pulley just short of the rope becoming locked on the pulley, as the unit was then apt to be damaged–not even taking into account the damage to the test setup. Needless to say, this required a good measure of skill by the test technician. The scale reading and the pulley radius provided the output torque. This output torque times the output speed divided by a constant gave the output power. Measuring the motor input electrical parameters gave the input power. As we know, output power divided by input power is the efficiency of the geared reducer.

Design engineers were usually located in manufacturing facilities, so through the product development, prototype, and initial manufacturing phases the engineer was right there where making the parts was actually occurring. Many questions would arise as to whether a part to be tested or inspected was “to specification.” It would often relate to whether a part that was specified to be hardened was in fact hard, and vice versa. Hardness-checking equipment usually wasn’t found in all of the locations that were visited by the product engineer, so one never went into an area where there would be geared parts and components without a hand file. With some experience it was possible to estimate the hardness of the part in question by the feel and the sound the file would make being moved across the part. While this was never used as the final word, this method could get to the bottom of an issue very quickly.

Again, we have come a long way in recent years, and engineers are always in a learning phase in order to grow professionally and better accomplish particular objectives in a more economical, efficient, accurate, and timely manner. But it doesn’t hurt to take a look back at how things were once done in order to gain a new appreciation of the tools, techniques, and technologies that are taken for granted today.

Previous articleQ&A with Jeffrey L. Lay
Next articleTerry McDonald: Site Safety
is president of Gears Plus, Inc., which provides consulting and engineering services. He is a member of AGMA and the Gear Research Institute, for which he sat on the board of trustees through 2004. Mihelick can be reached at (864) 944-8999, or send e-mail to