Date of download: 10/27/2017 Copyright © ASME. All rights reserved. From: Designing Microstructural Architectures With Thermally Actuated Properties Using Freedom, Actuation, and Constraint Topologies J. Mech. Des. 2013;135(6):061004-061004-10. doi:10.1115/1.4024122 Figure Legend: 2D microstructural architecture designs (a) and (b) that consist of unit cells made up of triangular sectors. These sectors (c) are designed using the geometric shapes of FACT (d).

Date of download: 10/27/2017 Copyright © ASME. All rights reserved. From: Designing Microstructural Architectures With Thermally Actuated Properties Using Freedom, Actuation, and Constraint Topologies J. Mech. Des. 2013;135(6):061004-061004-10. doi:10.1115/1.4024122 Figure Legend: A parallel flexure system's three DOFs (a)–(c) and its freedom space (d)

Date of download: 10/27/2017 Copyright © ASME. All rights reserved. From: Designing Microstructural Architectures With Thermally Actuated Properties Using Freedom, Actuation, and Constraint Topologies J. Mech. Des. 2013;135(6):061004-061004-10. doi:10.1115/1.4024122 Figure Legend: The system's complementary freedom and constraint space pair (a). The flexible constraints lie within the system's constraint space (b).

Date of download: 10/27/2017 Copyright © ASME. All rights reserved. From: Designing Microstructural Architectures With Thermally Actuated Properties Using Freedom, Actuation, and Constraint Topologies J. Mech. Des. 2013;135(6):061004-061004-10. doi:10.1115/1.4024122 Figure Legend: The system's actuation space (a). Selecting thermally actuated constraints from within the actuation space (b). Selectively heating each thermally actuated constraint by different temperatures causes the stage to move with various combinations of its DOFs (c).

Date of download: 10/27/2017 Copyright © ASME. All rights reserved. From: Designing Microstructural Architectures With Thermally Actuated Properties Using Freedom, Actuation, and Constraint Topologies J. Mech. Des. 2013;135(6):061004-061004-10. doi:10.1115/1.4024122 Figure Legend: A blank 2D lattice for synthesizing thermally actuated microstructural architectures (a) and a general design space sector for achieving a microstructural architecture with a negative-thermal expansion coefficient (b)

Date of download: 10/27/2017 Copyright © ASME. All rights reserved. From: Designing Microstructural Architectures With Thermally Actuated Properties Using Freedom, Actuation, and Constraint Topologies J. Mech. Des. 2013;135(6):061004-061004-10. doi:10.1115/1.4024122 Figure Legend: Two negative-thermal-expansion sectors with actuation elements that do not lie within the system's actuation space (a) and (b). The sectors' unit cells (c) and (d).

Date of download: 10/27/2017 Copyright © ASME. All rights reserved. From: Designing Microstructural Architectures With Thermally Actuated Properties Using Freedom, Actuation, and Constraint Topologies J. Mech. Des. 2013;135(6):061004-061004-10. doi:10.1115/1.4024122 Figure Legend: A sector example with no flexure bearing elements (a) and its unit cell (b).

Date of download: 10/27/2017 Copyright © ASME. All rights reserved. From: Designing Microstructural Architectures With Thermally Actuated Properties Using Freedom, Actuation, and Constraint Topologies J. Mech. Des. 2013;135(6):061004-061004-10. doi:10.1115/1.4024122 Figure Legend: Parameters necessary to calculate the thermal expansion coefficient of a unit cell, which is modeled as small rigid bodies (shown in black) connected by flexible elements

Date of download: 10/27/2017 Copyright © ASME. All rights reserved. From: Designing Microstructural Architectures With Thermally Actuated Properties Using Freedom, Actuation, and Constraint Topologies J. Mech. Des. 2013;135(6):061004-061004-10. doi:10.1115/1.4024122 Figure Legend: Parameters and conventions necessary to construct Eq. (3) for a general microstructural architecture

Date of download: 10/27/2017 Copyright © ASME. All rights reserved. From: Designing Microstructural Architectures With Thermally Actuated Properties Using Freedom, Actuation, and Constraint Topologies J. Mech. Des. 2013;135(6):061004-061004-10. doi:10.1115/1.4024122 Figure Legend: Dimensions for the microstructural architecture (a). An ale3d mesh of the deformed architecture when subject to an increase in temperature (b).

Date of download: 10/27/2017 Copyright © ASME. All rights reserved. From: Designing Microstructural Architectures With Thermally Actuated Properties Using Freedom, Actuation, and Constraint Topologies J. Mech. Des. 2013;135(6):061004-061004-10. doi:10.1115/1.4024122 Figure Legend: Comparison of this architecture's thermal expansion coefficient calculated using FEA verses the analytical tool of this paper