This paper treats the first-order kinematic properties of three dimensional motions with any number of freedoms from one to five. A method is presented for obtaining the canonical coordinates, the instantaneous invariants, the loci of the instantaneous screws, the canonic form of the equation of motion and its series expansion. Using this method we obtain entirely new results for three, four and five-degree-of-freedom motions, and verify some known results for one, two and three-degree-of-freedom motions.

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