LinkEdit: interactive linkage editing using symbolic kinematics

We present a method for interactive editing of planar linkages. Given a working linkage as input, the user can make targeted edits to the shape or motion of selected parts while preserving other, e.g., functionally-important aspects. In order to make this process intuitive and efficient, we provide a number of editing tools at different levels of abstraction. For instance, the user can directly change the structure of a linkage by displacing joints, edit the motion of selected points on the linkage, or impose limits on the size of its enclosure. Our method safeguards against degenerate configurations during these edits, thus ensuring the correct functioning of the mechanism at all times. Linkage editing poses strict requirements on performance that standard approaches fail to provide. In order to enable interactive and robust editing, we build on a symbolic kinematics approach that uses closed-form expressions instead of numerical methods to compute the motion of a linkage and its derivatives. We demonstrate our system on a diverse set of examples, illustrating the potential to adapt and personalize the structure and motion of existing linkages. To validate the feasibility of our edited designs, we fabricated two physical prototypes.