ON THE SHAFT LOCATIONS OF 2 CONTRA-ROTATING COUNTERWEIGHTS FOR BALANCING SPATIAL MECHANISMS

It has been shown in a previous work that a frequency term of the shak ing force of spatial mechanisms, whose hodograph is proved to be an el lipse, can be eliminated by a pair of contra-rotating counterweights. In this work, it is found that the relevant frequency term of the shak ing moment is minimized if the balancing shafts are coaxial at the cen tre of a family of ellipsoids, called isomomental ellipsoids, with res pect to (w.r.t.) any point on an ellipsoid, as is also the root mean s quare (r.m.s.) of the relevant frequency term of the shaking moment. I t can also be minimized even though the location of either shaft, but not both, is chosen arbitrarily on a plane. The location of the second shaft is then determinate. In order to locate the centre, a derivatio n for the theory of isomomental ellipsoids of a frequency term of the shaking moment of spatial mechanisms is given. It is shown that the r. m.s, of a frequency term shaking moment of a spatial mechanism w.r.t. the concentric centre of the isomomental ellipsoids is the minimum. Ex amples of a seven-link 7-R spatial linkage and a spatial slider-crank mechanism are included.