the broaches are mounted; the fixture is often referred to as a "pot". The pot is designed to hold multiple broaching tools concentrically over its entire length. The broach is held stationary while the workpiece is pushed or pulled through it. This has replaced hobbing for some involute gears and cutting external splines and slots. Straddle broaches use two slab broaches to cut parallel surfaces on opposite sides of a workpiece in one pass. This type of broaching holds closer tolerances than if the two cuts were done independently. It is named after the fact that the broaches "straddle" the workpiece on multiple sides. Internal broaches Solid broaches are the most common type; they are made from one solid piece of material. For broaches that wear out quickly shell broaches are used; these broaches are similar to a solid broach, except there is a hole through the center where it mounts on an arbor. Shell broaches cost more initially, but save the cost overall if the broach must be replaced often because the pilots are on the mandrel and do not have to be reproduced with each replacement. Modular broaches are commonly used for large internal broaching applications. They are similar to shell broaches in that they are a multi-piece construction. This design is used because it is cheaper to build and resharpen and is more flexible than a solid design. A common type of internal broach is the keyway broach (C & D). It uses a special fixture called a horn to support the broach and properly locate the part with relation to the broach. A concentricity broach is a special type of spline cutting broach which cuts both the minor diameter and the spline form to ensure precise concentricity. The cut-and-recut broach is used to cut thin-walled workpieces. Thin-walled workpieces have a tendency to expand during cutting and then shrink afterward. This broach overcomes that problem by first broaching with the standard roughing teeth, followed by a "breathing" section, which serves as a pilot as the workpiece shrinks. The teeth after the "breathing" section then include roughing, semi-finishing, and finishing teeth. Design For defining the geometry of a broach an internal type is shown below. Note that the geometries of other broaches are similar. where: P = pitch RPT = rise per tooth nr = number of roughing teeth ns = number of semi-finishing teeth nf = number