By addition of counterweights to the moving links of a linkage, supported by an elastically mounted frame, it is possible to reduce the frame vibration induced by the resulting forces and moments of the linkage on the frame. Determining the counterweights that yield a maximal reduction in frame vibration is a nonlinear optimization problem. This paper shows that this optimization problem can be reformulated as a convex problem, i.e. a nonlinear optimization problem that has a unique (global) optimum. This methodology is general but developed here for a planar four-bar linkage. For the particular example considered here, a robustness analysis shows a significant reduction of frame vibration even for drive speeds and mounting parameters other than those considered during the counterweight design.
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