This paper is the first of a series of papers developing a theory for the articulation of planar robots. Here, end effectors are considered to be moving on specified trajectories regardless of orientation, which is considered to be a free parameter, and which together with the remaining link orientations can be used to flex and hence articulate the arms to avoid interference. The theory is based on the geometry of the robots and workspace structures. An affine transformation is introduced for determining the relative location of pairs of links which are modeled by line segments.

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