A method for the driving torque, shaking moment, and shaking force balancing is given as individual or combined problems for all of the four-link mechanisms: the four-bar, the slider-crank, the inverted slider-crank, and the oscillating block mechanism. The “method of linearly independent vectors” of Berkof and Lowen is extended to the shaking moment and driving torque functions. These tools are combined to completely eliminate shaking force and shaking moment with the addition of a physical negative mass. Specified values of driving torque can be met exactly in up to three positions or in the least-square sense for the full cycle while maintaining shaking force balance. For shaking moment, up to five specified moments or a cyclic moment in the least-square sense can also be obtained without, however, an accompanying shaking force balance.

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