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The immobilization of nonrigid objects is a relatively unexplored area in grasp mechanics. In this paper, we consider the immobilization of freely moving serial chains of n hinged polygons using frictionless point fingers. We first set this problem in the context of classical grasping theory by showing that chain immobilization can only be achieved with equilibrium grasps. Then, we describe two immobilization approaches based on first- and second-order geometric effects. Based on curvature effects, chains of n ≠ 3 hinged polygons with nonparallel edges can be immobilized by n + 2 frictionless point fingers. Serial chains of three hinged polygons form an exception to this rule. Based on first-order geometric effects, we describe how to immobilize any chain of n hinged polygons with only one extra contact for the entire chain, using a total of n + 3 frictionless point fingers. Moreover, the immobilizing grasps are robust with respect to small contact placement errors. The results are illustrated with examples and described as readily implementable procedures.