This work intends to deal with the type synthesis problem of deployable/foldable articulated mechanisms. The type synthesis in this kind of mechanism design can be factorized into two stages: the first stage is the topological synthesis of which the properties of mechanism are reflected by the graph; the second stage is the kinematic synthesis which aims at finding a set of mechanisms with the desired kinematic properties. According to the folded morphology, the compact form for deployable units are first classified into three categories: linear compact structure, planar compact structure and hybrid compact structure. Then we can enumerate the topological structures of these three categories and synthesize their combinations. Different from kinematic synthesis of general industrial robot which amounts to find the set of robotic mechanisms such that the end-effector of which has the desired mobility, the kinematic synthesis of deployable mechanism is to find out the set of mechanisms which can be folded onto the desired compact form in which the mechanism is taking up the minimum geometric volume. If a mechanism has at least one inverse solution to the desired compact form for the given set of parameters and there is finite mobility between the deployed and folded configurations, that is the mechanism we are looking for.
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