  We present an optimization-based design process that can generate the best
insertion-based joints with respect to different errors, including manipulation
error, manufacturing error, and sensing error. We separate the analysis into
two stages, the insertion and the after-insertion stability. Each sub-process
is discretized into different modes of contacts. The transitions among the
contact modes form a directed graph and the connectivity of the graph is
achieved and maintained through the manipulation of the socket edge-angle and
peg contact-point locations. The analysis starts in 2D with the assumption of
point-edge contacts. During the optimization, the edges of the socket are
rotated and the points on the peg are moved along the edges to ensure the
successful insertion and the stability after insertion. We show in simulation
that our proposed method can generate insertion-based joints that are tolerant
to the given errors. and we present a few simple 3D projections to show that
the analysis is still effective beyond 2D cases.
