Two sector gears, located at the ends of links 1 and 2 , are engaged together and rotate about \(O_{1}\) and \(O_{2}\), as shown in Fig. 1.95. If links 1 and 2 are connected to springs \(k_{1}\) to \(k_{4}\) and \(k_{t 1}\) and \(k_{t 2}\) as shown, find the equivalent torsional spring stiffness and equivalent mass moment of inertia of the system with reference to \(\theta_{1}\). Assume

(a) the mass moment of inertia of link 1 (including the sector gear) about \(O_{1}\) is \(J_{1}\) and that of link 2 (including the sector gear) about \(O_{2}\) is \(J_{2}\), and

(b) the angles \(\theta_{1}\) and \(\theta_{2}\) are small.

Transcribed Image Text:

Sector gear 2 Link 2 K12 Sector gear 1 Link 1 m18 000 P21 01 k1 FIGURE 1.95 Two sector gears.