Synthesis of precision serial flexure systems using freedom and constraint topologies (FACT)

Hopkins, Jonathan B.; Culpepper, Martin L.

doi:10.1016/j.precisioneng.2011.04.006

Cited by 86 publications

(74 citation statements)

References 25 publications

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“…This formulation has been previously presented by Su (2011). Also see similar work by Hopkins (2007b); Hopkins and Culpepper (2011). By applying a column-wise reduction, we can easily obtain a set of independent r = rank(T ) twists that forms the basis of the freedom space.…”

Section: Serial Chains Of Flexure Primitivesmentioning

confidence: 85%

Type synthesis of freedom and constraint elements for design of flexure mechanisms

2013

Mech. Sci.

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Abstract. In this paper, we present the type synthesis of freedom and constraint elements for design of general flexure mechanisms. As an important step in the conceptual design stage, the goal of type synthesis is to qualitatively determine the topology or connectivity of flexure elements and rigid bodies in a mechanism. The synthesis procedure presented here is based on a recently emerging screw theory based approach for flexure mechanisms. We first categorize a list of commonly used atomic flexure primitives including blades, wires, notches and bellow springs etc. We then derive their twist and wrench matrices that mathematically represent their freedom and constraint spaces. The synthesis procedure rigorously follows screw algebra. Freedom elements including R-joints and P-joints are defined as basic motion elements that allow a single rotation or a single translation. By using parallel structures of these flexure primitives, eleven designs of R-joints and eight designs of P-joints are systematically synthesized. As a duality, constraint elements including P-constraints and R-constraints remove a single translation or rotation. In contract to freedom elements, we synthesized serial chains of flexure primitives and obtained six designs of P-constraints and three designs of R-constraints. These freedom and constraint elements form a catalogue of basic building blocks for designing more complex flexure mechanisms. At last we utilize four design examples to demonstrate how to synthesize hybrid structures with serial and parallel combination of these elements.

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Section: Serial Chains Of Flexure Primitivesmentioning

confidence: 85%

Type synthesis of freedom and constraint elements for design of flexure mechanisms

2013

Mech. Sci.

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“…Although the mathematics of these principles have been applied to rigid body mechanisms for many years, only recently have these principles been applied to the synthesis of parallel Culpepper, 2006, 2010;Hopkins, 2007;Su et al, 2009;Su and Tari, 2010) and serial flexure systems (Hopkins, 2010;Hopkins and Culpepper, 2011;Su, 2011) These principles will be extended in later sections to enable designers to analyse and design hybrid flexure systems and elements using FACT.…”

Section: Fundamental Principlesmentioning

confidence: 99%

“…If, however, the sum of the number of DOFs within each selected intermediate freedom space from step 3 exceeds the number of total independent twist vectors within all of these spaces combined, the system is under-constrained (Blanding, 1999;Hopkins and Culpepper, 2011). The intermediate rigid bodies of an under-constrained system often possess DOFs that are not constrained even when the final system's stage is held fixed relative to its ground.…”

Section: Synthesizing Serial Flexure Systemsmentioning

confidence: 99%

“…This theory is an extension of the Freedom and Constraint Topologies (FACT) synthesis approach (Hopkins and Culpepper, 2006;Hopkins, 2007). This approach utilizes a comprehensive library of geometric shapes, similar to the shapes formed by the constraint lines within the examples of Fig.…”

Section: Introductionmentioning

confidence: 99%

“…These shapes visually embody the mathematics of screw theory (Ball, 1900;Phillips, 1984Phillips, , 1990 and enable designers to rapidly consider and compare a multiplicity of solution concepts in an intuitive way. The shapes of FACT have previously been applied to the design of parallel flexure systems , serial flexure systems (Hopkins and Culpepper, 2011), parallel flexure elements (Hopkins, 2012;, and serial flexure elements (Hopkins, 2013). In this paper, we briefly review the principles of these publications and explain how these principles can be adapted and applied to the design of hybrid flexure systems and elements.…”

Section: Introductionmentioning

confidence: 99%

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Designing hybrid flexure systems and elements using Freedom and Constraint Topologies

Hopkins

2013

Mech. Sci.

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Abstract. In this paper we introduce the principles necessary to synthesize hybrid flexure systems and elements. Flexure systems consist of rigid bodies that are joined together by flexure elements that elastically deform to guide the system's rigid bodies with desired degrees of freedom (DOFs). The principles introduced here for synthesizing hybrid flexure systems and elements are extensions of the Freedom and Constraint Topologies (FACT) synthesis approach. FACT utilizes a comprehensive library of geometric shapes from which designers can rapidly consider and compare a multiplicity of flexure concepts that achieve any desired set of DOFs. Prior to this paper, designers primarily used these shapes to synthesize parallel and serial flexure systems and elements. With this paper, designers may now use these same shapes to synthesize more general flexures that consist of various combinations of parallel and serial systems and elements (i.e., hybrid configurations). As such, designers can access a larger body of flexure solutions that satisfy demanding design requirements. Instructions for helping designers utilize or avoid the advantages and challenges of over-, under-, and exactconstraint are also provided. Hybrid systems and elements are analysed and designed as case studies.

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Mechanisms

2013

Handbook of Compliant Mechanisms

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Synthesis of precision serial flexure systems using freedom and constraint topologies (FACT)

Cited by 86 publications

References 25 publications

Type synthesis of freedom and constraint elements for design of flexure mechanisms

Type synthesis of freedom and constraint elements for design of flexure mechanisms

Designing hybrid flexure systems and elements using Freedom and Constraint Topologies

Mechanisms

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