Motion Types of 2-DOF Hybrid Kinematic Chains

Hybrid (parallel-serial) kinematic chains with two degrees of freedom (DOFs) can serve as 2-DOF mechanisms or as a part of other mechanical systems with three or more DOFs. Unlike 2-DOF serial chains, the motion type (a set of possible instantaneous motions) of a hybrid chain can vary when the chain changes its configuration. This article aims to illustrate this behavior and discusses different motion types of 2-DOF hybrid chains. First, by using screw theory and Hunt’s classification, we divide all possible instantaneous motions into six distinct types (one general and five special) based on their twist systems. Next, we examine these types and their corresponding hybrid chains. We show the twist system of a hybrid chain can change its pose, shape, and type, in contrast to 2-DOF serial chains, where the twist system remains persistent. For each motion type, we present an example of a 2-DOF hybrid chain.