Collaborative Research: Variational Kinematic Geometry and Task Driven Mechanism Design in VR Environment

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Abstract The research objective of this award is to develop a new, constraint based paradigm for task-driven mechanism design in a virtual environment. Concepts in variational geometry for constraint based geometric modeling will be extended from geometric domain to kinematic domain for representing and resolving kinematic constraints that define a given motion. This facilitates a constraint based analysis, classification, and synthesis of rigid body motions by applying and adapting existing methods in the field of computational shape analysis. Deliverables include: (1) a B-spline motion generation tool for specifying a motion task; (2) a novel motion trajectory analysis tool for converting a prescribed planar or spherical motion into a set of geometric primitives; (3) a database of basic planar or spherical mechanism constructs sorted by the geometric constraints that they can generate; and (4) an interactive, virtual-reality (VR) enabled design environment that solves the problem of mechanism design as a shape identification and retrieval problem. If successful, the results of this research will lead to a new, multidisciplinary framework called "Variational Kinematic Geometry." It will make the often elusive task of concept generation in mechanism design more tractable. The proposed design environment will be capable of solving highly complex motion generation problems without requiring advanced knowledge of kinematics from the user. The results will be disseminated through the software distribution to other fields such as biomechanics, structure chemistry and protein kinematics, as well as micro- and nano-systems, in which kinematics plays an important role. The virtual design tool will be used as an education tool for teaching and learning spatial visualization and reasoning and for exploring the interplay between geometry and motion. The education and outreach activities of the proposed effort will help promote interest for science and engineering from underrepresented groups and high school students.