The equations of motion of hybrid robots are linearized (fully or partially) using the concept of linearity number (LN). The definition of LN is modified slightly to yield the torque fluctuation number (TFN). TFN is utilized to minimize the inputtorque fluctuations of any 1 d.o.f. mechanism, which may be under the influence of external loads. Linearization or smoothening of the input torque is achieved by minimizing LN or TFN as much as the design constraints allow. It is shown that both LN andTFN can always be obtained in "closed-form" using similar computation techniques; and they can be minimized "analytically" leading to "closed-form" solutions for the "global" minimum and the corresponding optimal inertial parameters.
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