High-quality hand-made furniture often employs intrinsic joints that geometrically interlock along mating surfaces. Such joints increase the structural integrity of the furniture and add to its visual appeal. We present an interactive tool for designing such intrinsic joints. Users draw the visual appearance of the joints on the surface of an input furniture model as groups of 2D regions that must belong to the same part. Our tool automatically partitions the furniture model into a set of solid 3D parts that conform to the user-specified 2D regions and assemble into the furniture. If the input does not merit assemblable solid 3D parts, our tool reports the failure and suggests options for redesigning the 2D surface regions so that they are assemblable. Similarly, if any parts in the resulting assembly are unstable, our tool suggests where additional 2D regions should be drawn to better interlock the parts and improve stability. To perform this stability analysis, we introduce a novel variational static analysis method that addresses shortcomings of the equilibrium method for our task. Specifically, our method correctly detects sliding instabilities and reports the locations and directions of sliding and hinging failures. We show that our tool can be used to generate over 100 joints inspired by traditional woodworking and Japanese joinery. We also design and fabricate 9 complete furniture assemblies that are stable and connected using only the intrinsic joints produced by our tool.