This paper investigates the motion and constraint ruled surfaces of the Schatz linkage by examining their geometric characteristics based on screw system analysis. The paper starts by revealing two assembly configurations in accordance with previous literature and examines the cycle phases of the coupler link. This leads to analysis of the motion ruled surface generated by the directrix along the coupler link with Euclidean invariants. The paper further investigates the screw system and its corresponding reciprocal screw and generates the constraint ruled surface in studying its geometry. The study is based on Euclidean invariants and presents intrinsic characteristics between motion and constraint rules surfaces and geometric parameters, revealing the special property of the Schatz linkage.

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