Workshop on 21st Century Kinematics; Washington, DC; 27-28 August 2011

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The purpose of this award is to support a workshop on 21st Century Kinematics, which will bring together experts and novices together to demonstrate the use of numerical algebraic geometry to solve current research problems in areas that are fundamental to advancing Kinematics. These areas are united by the challenge of solving even larger systems of polynomials, specifically the analysis and synthesis of mechanisms and robots, compliant mechanisms, and tensegrity and cable-driven systems. In each case, the challenge of formulating and solving these polynomial systems is a significant obstacle. The workshop will explore new results in numerical algebraic geometry and improved computation that have the potential to provide tools for rapid derivation, analysis and solution of complex polynomial systems. This is critical to the advancement of mechanisms and robotics research into the 21st century. The intellectual merit of this workshop award centers on advancing the capabilities for research into the design of complex and innovative mechanical systems by introducing advanced techniques of numerical algebraic geometry to the mechanisms and robotics research community.If successful, this workshop will provide an opportunity to build on past successes in the development of robotic systems, compliant and micro-electromechanical systems by using new mathematical formulations. In the 21st century, advances in information-driven systems and mechatronics demand even more innovation in mechanisms and robotics, in order to transform 'bits of information' into the 'bits of physical activity' needed to manipulate, transport and deliver goods and services. The presentations will be assembled into course notes to form the foundation of graduate courses in universities around the country that will balance theory with practice, and fundamental science with design innovation. This workshop has the potential to rapidly disseminate the computational tools of numerical algebraic geometry to a large number of researchers, and reset the expectations of what is possible in the design of increasingly complex mechanical systems.