Special Cases

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Section 5.3 Special Cases

We can identify three special cases of ``instantaneous’’ motion:

Case 1. If, at a given time, \(\bom_{\cB /\cA}= \bze\) and there exists a point of \(\cB\) with zero velocity, then \(\cB\) is instantaneously at rest relative to \(\cA\text{:}\) \(\vel_{P\in\cB /\cA} =\bze\) for all \(P\text{.}\) Keep in mind that the acceleration field of \(\cB\) may not be zero at this instant.

Case 2. If, at a given time, \(\bom_{\cB /\cA}= \bze\) and there exists a point of \(\cB\) with non-zero velocity, then the velocity field of \(\cB\) is that of an instantaneous translational motion along \(\Delta\text{.}\)

Case 3. If, at a given time, \(\bom_{\cB/\cA}\) is not zero, yet the pitch \(p\) is zero, then the velocity field of \(\cB\) is that of an instantaneous rotational motion about axis \(\Delta = (I, \bom_{\cB / \cA})\text{.}\) Point \(I\) is defined by equation (5.1.3). In this case, axis \(\Delta\) is referred to as the instantaneous axis of rotation of \(\cB\text{.}\) Conversely, if there exists a point \(I\) such that \(\vel_{I\in\cB /\cA}= \bze\text{.}\) ¹, then \(I\) is necessarily located on the instantaneous axis of rotation of \(\cB\text{.}\)