(a) Draw the free-body diagram of the gear and shaft mechanism shown below (Figure 2.53).

(b) Find expressions for the gear ratio, \(N\), and the angular displacements, \(\theta_{a}(t)\) and \(\theta_{b}(t)\).

(c) Find the equivalent stiffness constant \(k_{e q}\) such that the algebraic model of the system is given by

\[\theta_{1}=\frac{T(t)}{k_{e q}}\]

where \(k_{e q}\) is a function of \(k_{1}, k_{2}, r_{a}\), and \(r_{b}\).

Transcribed Image Text:

A 0a Fixed End 0b T(t) Figure 2.53 A gear and shaft mechanism. 01 k