It is shown that the RMS shaking moment of unbalanced planar mechanisms is constant with respect to all points along certain concentric ellipses (isomomental ellipses) in the mechanism plane. The RMS shaking moment decreases for reference points located on ellipses of decreasing size, and the center of this family of ellipses represents the point about which the RMS shaking moment of the mechanism is a minimum. This theory provides a useful tool for evaluating the effect of full force balancing on the RMS shaking moment of a given planar mechanism.

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