2 nd international and 17 th National Conference on Machines and Mechanisms iNaCoMM2015-157 Data-Driven Kinematics: Unifying Synthesis of Planar Four-Bar Linkages via Motion Analysis Anurag Purwar, Q. Jeffrey Ge Abstract This paper presents a novel data-driven approach for kinematic synthesis of planar four-bar linkages consisting of revolute (R) or prismatic (P) joints by extracting the ge- ometric constraints of a motion. The approach unifies the often elusive type synthesis problem with dimensional synthesis and for a given motion determines the best com- binations of R- and P-joints in a four-bar linkage and their dimensions by analyzing a given motion. The underlying formulation is based on concepts of planar quaternions, kinematic mapping, and data-fitting. By formulating the kinematic constraints of pla- nar four-bar linkages in a unified form and then fitting the constraints with the given motion data in the image space of planar displacements, we obtain the best type and the dimensions of the linkages. The results will be demonstrated via MotionGen, an intuitive iOS and Android app that implements this approach and allows designers to synthesize linkages for the motion generation problem. Keywords: Planar-Four Bar Linkage Synthesis and Analysis, Planar Quaternions, Kinematic Mapping, Data Fitting, Reverse Engineering 1 Introduction The overarching goal of our current research is to bring together the Computational Shape Analysis and Design Kinematics to develop a new data-driven paradigm for kinematic syn- thesis of mechanical motion generating devices. We seek to establish a new computational foundation for simultaneous type and dimensional synthesis of such devices. This includes (1) the development of “freeform” or unified versions of design equations that span broad classes of mechanisms; (2) the development of unified algorithms for data-driven simul- taneous type and dimensional synthesis of planar, spherical and spatial mechanisms. This effort to reformulate design kinematics to unify the type and dimensional synthesis could have a transformative effect on mechanism design in terms of both research and design practice. In this paper, our focus is on presenting unified synthesis approach for the planar four-bar motions, which leads to a simultaneous determination of both type and dimensions for a given motion. The algorithm developed is highly amenable to efficient implementation that permits real-time computation. This is further demonstrated via an iOS and Android MotionGen app developed at Stony Brook University. This intuitive app facilitates solving complex motion generation problems without requiring advanced knowledge of kinematics from the user. 0 Anurag Purwar (Corresponding author), Research Associate Professor Computer-Aided Design Innovation Lab, Mechanical Engineering, Stony Brook University, Stony Brook, NY, anurag.purwar@stonybrook.edu . Q. Jeffrey Ge, Professor and Interim Chair Computational Design Kinematics Lab, Mechanical Engineering, Stony Brook University, Stony Brook, NY, qiaode.ge@stonybrook.edu 1