Mechanisms are ubiquitous in our daily lives, and the motion they are able to transmit is often a critical part of their function. While fabrication from a virtual model can be done relatively easily in a fab lab, creating or customizing a model according to functional specifications remains a challenging task. We focus on a fascinating application: drawing machines. Devices such as the popular Spirograph can easily generate intricate patterns from an assembly of simple mechanical elements. Designing such machines, however, is made particularly tedious by the complex influence each configuration parameter has on the final drawing. We propose a novel constrained exploration method that enables a user to easily explore feasible drawings by directly indicating pattern preferences at different levels of control. The user starts by selecting a target pattern with the help of construction lines and rough sketching, and then fine-tunes it by prescribing geometric features of interest directly on the drawing. The designed pattern can then be directly realized with an easy-to-fabricate drawing machine. The key technical challenge is to allow the user to effectively explore the high dimensional configuration space of such fabricable machines. To this end, we propose a novel method that dynamically reparam-eterizes the local configuration space in order to allow the user to explore drawing variations while preserving user-specified feature constraints. We tested our framework on several examples, conducted a user study, and fabricated a sample of the designed examples.