We propose a framework for optimizing a planar parallel-jaw gripper for use with multiple objects. While optimizing general-purpose grippers and contact locations for grasps are both well studied, co-optimizing grasps and the gripper geometry to execute them receives less attention. As such, our framework synthesizes grippers optimized to stably grasp sets of polygonal objects. Given a fixed number of contacts and their assignments to object faces and gripper jaws, our framework optimizes contact locations along these faces, gripper pose for each grasp, and gripper shape. Our key insights are to pose shape and contact constraints in frames fixed to the gripper jaws, and to leverage the linearity of constraints in our grasp stability and gripper shape models via an augmented Lagrangian formulation. Together, these enable a tractable nonlinear program implementation. We apply our method to several examples. The first illustrative problem shows the discovery of a geometrically simple solution where possible. In another, space is constrained, forcing multiple objects to be contacted by the same features as each other. Finally a toolset-grasping example shows that our framework applies to complex, real-world objects. We provide a physical experiment of the toolset grasps.

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