ABSTRACT
In designs different from those shown in Figure 1 it may prove convenient to have the shoe pivoted about a point at a radial distance R on the axis of symmetry, such as point A in Figure 4. The moment Mp due to the pressure on the lining is zero about point A because of the symmetry of the shoe about this point. No such symmetry exists for the friction moment Mƒ, however, so from the incremental moment due to friction
it follows that
(1-5)
where 0=θ2 – θ1 The expression in equation (1-5) may be simplified by observing that the symmetry of the shoe about A requires that
(1-6)
where φ0 is the angle subtended by the lining. Substitution of these values into equation (1-5) leads to
(1-5a)
which suggests that moment Mf will vanish if the shoe is pivoted at
(1-7)
Upon plotting R/r we obtain Figure 5, wherein the ratio increases smoothly from 1.0 at 0=0 to 1.273 at 0=π rad.=180°. This clearly indicates that it is impossible to find a pivot point for which Mƒ=0 for an internal linearly acting shoe. This conclusion is, of course, unaffected by the
sign reversal found in the expression (R cos θ-r) when equation (1-5a) is applied to an internal shoe. The sign reversal simply changes the direction of rotation implied by a positive value of Mƒ, as was discussed in an earlier section.
