The object of the paper is to contribute some new and fundamental concepts to the mechanics of machinery. The scope is limited to the subject of brakes, which was found to have been somewhat neglected in the past. To make the paper self-contained, some well-established laws on sliding friction are given as groundwork. Attention is called to facts that have been ignored in some textbooks because of apparent insignificance, although they are of vital importance in the special subject of brake design.
An analysis of the force relations for simple block-brakes is given first, with the intention to make clear that the equations so far available for designers are not sufficiently accurate for brakes such as are used on modern motor-vehicles and railroad coaches.
Attention is called to the fact that the wear on brake liners is not necessarily an indication of high pressures but more accurately is a function of the geometric relation between the shoe and the drum. It is acknowledged that for flexible liners the center of pressure is nearly in that horizontal axis where the wear is maximum, but it is proved that after the liner is glazed high local-pressures are very likely to occur momentarily where the wear is very small. Attention is called also to some difficulties encountered in adjusting brakes as well as in manufacturing them.
Formulas are given for the study of the self-energizing characteristics of brakes. These should be very helpful in connection with four-wheel-brake designs, because it was recognized very early that with doubling the number of brakeshoes very high foot-pressures were required to obtain satisfactory retardation.
An empirical rule frequently used for determining roughly the arc of contact is discussed but is found insufficient for modern, more exacting requirements. Instead, a new graphical method is given. This new method is based on an analysis of the pressures and is formulated so that high pressures with their accompanying evils are avoided. Adherence to the method given leads to the more modern brake-design with multiple shoes. In the analytical work, limiting conditions are extensively discussed. These mathematical discussions serve as groundwork for the recommended graphical method. Some advantages of brakes with three shoes are given. One of these is the large arc of contact that can be obtained.
An effort is made to prove that squeaking, chattering and grabbing are not necessarily a result of a variation in the coefficient of friction. Diagrams are given to show that pressures are just as likely as the coefficient of friction to cause this trouble. In modern designs, a high friction-coefficient is desired, and means are provided to keep it constant; therefore, even pressure-distribution is stated to be important.
In conclusion, the railroad type of brake is discussed. It is pointed out that pressures cannot accumulate in it as in other types; therefore, this type is recommended for applications where chattering is likely to be pronounced because of the existence of backlash and where great mechanical advantage is of lesser importance.


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