This paper presents tools and methods to design cylindrical and conical developable mechanisms from flat, planar patterns. Equations are presented that relate the link lengths and link angles of planar and spherical mechanisms to the dimensions in a flat configuration. These flat patterns can then be formed into curved, developable mechanisms. Guidelines are established to determine if a mechanism described by a flat pattern can exhibit intramobile or extramobile behavior. A developable mechanism can only potentially exhibit intramobile or extramobile behavior if none of the links extend beyond half of the flat pattern. The behavior of a mechanism can change depending on the location of the cut of the flat pattern. Different joint designs are discussed including lamina emergent torsional (LET) joints. Physical examples are presented.

Origami patterns have been used in the design of deploy- able arrays. In engineering applications, paper creases are often replaced with surrogate folds by providing a hinge-like function to enable motion. Overconstraint ob- served in multi-vertex origami patterns combined with imperfect manufacturing may cause the resulting mech- anisms to bind. The removal of redundant constraints de- creases the likelihood of binding, may simplify the over- all system, and may decrease the actuation force by re- ducing friction and other resistance to motion. This pa- per introduces a visual and iterative approach to elim- inating redundant constraints in origami-based mecha- nisms through joint removal. Several techniques for joint removal are outlined and illustrated to reduce overcon- straints in origami arrays.

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