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2045 |
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A Quantitative, Constraint-based Design Method for Multi-axis Flexure Stages for Precision Positioning Equipment |
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Equipment, Machines & Instruments: Analysis & Modeling |
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The intent of this paper is to demonstrate new quantitative design methods and complimentary design tools for constraint-based design (CBD) of complex precision flexure stages. The essence of constraint-based design is the process of selecting and arranging machine elements (e.g. flexures) in a geometric layout that endows a device with desired positioning and alignment performance [1]. Constraint-based design principles are central to precision engineering as the layout of a machine’s constraints set limits on device’s degrees-of-freedom, stiffness, load capacity, repeatability, stability, etc… The problem is that constraint-based design, in its present state, is based upon visualization and therefore it is difficult to design multi-piece parallel flexure devices that move in more than three axes. The purpose of this paper is to demonstrate new constraint-based theory, modeling and design tools that enable designers to more easily synthesize complex flexure designs (4 degrees-of-freedom or more) and then assess their performance characteristics. The practical implications are that these design tools and the quantitative constraint-based design approach will enable the creation of new flexure devices and improvement or adaptation of conventional flexure designs.
For over 100 years, CBD has been practiced by using a combination of geometric visualization techniques, practical experience and rules of thumb. These conventional techniques are easily used to create precision flexure stages wherein the motions are planar (x, y and theta-z). Examples are readily found in optical adjustments, fixtures, lithography machines, instruments and positioning stages for high-resolution microscopes. A great deal of CBD experience, and sometimes trial-and-error, are required to design flexures that are simultaneously capable of planar and non-planar (theta-x, theta-y and z) motions. Except for a few exceptions, experience is not enough to design stages that must move in four or more degrees-of-freedom. The ability to know how to arrange constraints in ways that add symmetry and stiffness to the system without affecting the desired degrees of freedom is almost impossible to obtain without some type of mathematical formulation. This paper provides a quantitative approach to constraint-based design and discusses the use of this theory in a constraint-based design tool (like FEA for constraint-based design). Efforts to embody the approach and theory in a virtual reality design tool will be discussed. This approach also enables the solution of persisting problems in constraint based design. For instance, the problem of coupled degrees-of-freedom could not be well-understood in a general sense before the aforementioned approaches. The application of this theory and the design tool will be demonstrated via case studies on the design of several parallel flexure devices.
1. D. L. Blanding, “Exact Constraint: Machine Design Using Kinematic Principles” (1999)
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