A systematic algorithm, for the complete position analysis of ''any'' single loop spatial mechanism, is introduced. The method yields four non-linear equations, with the least possible total degree. These equations are transformed into algebraic ones, which may be solved, analytically, based upon the concept of resultants. The solutions are free from extraneous roots, since such roots are identified and extracted by the proposed techniques. An algorithm, for the efficient position analysis of mechanisms with parallel or perpendicular joint axes and/or zero link lengths and offsets, is also given. (C) 1997 Elsevier Science Ltd.