Engineering design requires many different types of gears and splines. Although these components are rather expensive, subject to direct wear, and difficult to replace, transmissions with gears and splines are required for two very simple reasons: 1) Motors have an unfavorable (disadvantageous) relation of torque to number of revolutions. 2)Power is usually required to be transmitted along a shaft.

An accurate and fast calculation method is developed to determine the value of a trigonometric function if the value of another trigonometric function is given. Some examples of conversion procedures for well-known functions in gear geometry are presented, with data for accuracy and computing time. For the development of such procedures the complete text of a computer program is included.

A widespread weakness of gear drawings is the requirements called out for carburize heat treating operations. The use of heat treating specifications is a recommended solution to this problem. First of all, these specifications guide the designer to a proper callout. Secondly, they insure that certain metallurgical characteristics, and even to some extent processing, will be obtained to provide the required qualities in the hardened gear. A suggested structure of carburizing specifications is give.

After shaping or hobbing, the tooth flanks must be either chamfered or duburred. Here it is paramount that the secondary burr produced will not be formed into the flank, but to the face of the gear, because during hardening, the secondary burr will straighten up and, due to its extreme hardness, will lead to excessive tool wear.

Profitable hard machining of tooth flanks in mass production has now become possible thanks to a number of newly developed production methods. As used so far, the advantages of hard machining over green shaving or rolling are the elaborately modified tooth flanks are produced with a scatter of close manufacturing tolerances. Apart from an increase of load capacity, the chief aim is to solve the complex problem of reducing the noise generation by load-conditioned kinematic modifications of the tooth mesh. In Part II, we shall deal with operating sequences and machining results and with gear noise problems.

Gears are toothed wheels used primarily to transmit motion and power between rotating shafts. Gearing is an assembly of two or more gears. The most durable of all mechanical drives, gearing can transmit high power at efficiencies approaching 0.99 and with long service life. As precision machine elements gears must be designed.

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.

Primitive gears were known and used well over 2,000 years ago, and gears have taken their place as one of the basic machine mechanisms; yet, our knowledge and understanding of gearing principles is by no means complete. We see the development of faster and more reliable gear quality assessment and new, more productive manufacture of gears in higher materials hardness states. We have also seen improvement in gear applications and design, lubricants, coolants, finishes and noise and vibration control. All these advances push development in the direction of smaller, more compact applications, better material utilization and improved quietness, smoothness of operation and gear life. At the same time, we try to improve manufacturing cost-effectiveness, making use of highly repetitive and efficient gear manufacturing methods.

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.

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.