The applicability and limitations of the present existence criteria for space mechanisms are discussed. The number synthesis technique is applied to the Kutzbach Criterion to identify all the possible simple loop, single degree of freedom space mechanisms which incorporate the known physically realizable pairs. An examination of the 138 kinds of space four-link mechanisms is made within the boundaries of practical realizability to identify the nine kinds of four-link mechanisms which are worthy of intensive study and application. In addition, the practical importance of the several known “special” space mechanisms which exist outside the Kutzbach Criterion is noted.

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