Freedom and constraint topologies (a.k.a., freedom, actuation, and constraint topologies; or simply FACT). [1] [2] [3] is a mechanical design framework developed by Dr. Jonathan B. Hopkins. The framework offers a library of vector spaces with visual representations to guide the analysis and synthesis of flexible systems. Flexible systems are devices, mechanisms, or structures that deform to achieve desired motion such as compliant mechanisms, flexures, soft robots, and mechanical metamaterials.
The FACT design approach was created in 2005 by Jonathan Brigham Hopkins while a Master’s student in Professor Martin L. Culpepper’s Precision Compliant Systems Laboratory at MIT. FACT was first published in a short conference paper in the 2006 proceedings of the 21st Annual Meeting of the American Society for Precision Engineering [4] and was later published in depth in Hopkins’ 2007 Master's thesis. [5] FACT has been expanded in later works such as Hopkins' 2010 PhD Thesis.
Other compliant mechanism design methods include generative design, pseudo-rigid-body analysis, [6] and other constraint-based and [screw theory]-based design approaches. [7] See the main article for pros and cons of kinematics and structural optimization.
FACT combines principles of screw theory, linear algebra, projective geometry, and exact-constraint design. The methodology employs a library of vector spaces derived from these principles and represented by geometric shapes. These shapes are categorized into freedom spaces, constraint spaces, and actuation spaces, each serving a unique purpose in the design process.
The FACT library allows traversal of the complete solution space of flexible systems for any combination of degrees of freedom. The rules of FACT vary depending on the configuration of the flexible system desired. Here are the basic steps to design a parallel flexure bearing.
Sometimes it may be desireable to over-constrain the system by adding redundant constraints within the constraint space. This adds stiffness and may be required for symmetry, which can improve thermal stability.
All flexible systems can be organized according to three primary configurations – parallel, serial, and hybrid. FACT alone covers parallel, serial, and some hybrid systems.
FACT is covered in various educational resources:
Freedom and constraint topologies (a.k.a., freedom, actuation, and constraint topologies; or simply FACT). [1] [2] [3] is a mechanical design framework developed by Dr. Jonathan B. Hopkins. The framework offers a library of vector spaces with visual representations to guide the analysis and synthesis of flexible systems. Flexible systems are devices, mechanisms, or structures that deform to achieve desired motion such as compliant mechanisms, flexures, soft robots, and mechanical metamaterials.
The FACT design approach was created in 2005 by Jonathan Brigham Hopkins while a Master’s student in Professor Martin L. Culpepper’s Precision Compliant Systems Laboratory at MIT. FACT was first published in a short conference paper in the 2006 proceedings of the 21st Annual Meeting of the American Society for Precision Engineering [4] and was later published in depth in Hopkins’ 2007 Master's thesis. [5] FACT has been expanded in later works such as Hopkins' 2010 PhD Thesis.
Other compliant mechanism design methods include generative design, pseudo-rigid-body analysis, [6] and other constraint-based and [screw theory]-based design approaches. [7] See the main article for pros and cons of kinematics and structural optimization.
FACT combines principles of screw theory, linear algebra, projective geometry, and exact-constraint design. The methodology employs a library of vector spaces derived from these principles and represented by geometric shapes. These shapes are categorized into freedom spaces, constraint spaces, and actuation spaces, each serving a unique purpose in the design process.
The FACT library allows traversal of the complete solution space of flexible systems for any combination of degrees of freedom. The rules of FACT vary depending on the configuration of the flexible system desired. Here are the basic steps to design a parallel flexure bearing.
Sometimes it may be desireable to over-constrain the system by adding redundant constraints within the constraint space. This adds stiffness and may be required for symmetry, which can improve thermal stability.
All flexible systems can be organized according to three primary configurations – parallel, serial, and hybrid. FACT alone covers parallel, serial, and some hybrid systems.
FACT is covered in various educational resources: