1. Date of download: 7/10/2016 Copyright © ASME. All rights reserved. From: Automated Generation of Linkage Loop Equations for Planar One Degree-of-Freedom Linkages, Demonstrated up to 8-Bar J. Mechanisms Robotics. 2015;7(1):011006-011006-8. doi:10.1115/1.4029306 Example Watt I linkage reaching a task position Figure Legend:

2. Date of download: 7/10/2016 Copyright © ASME. All rights reserved. From: Automated Generation of Linkage Loop Equations for Planar One Degree-of-Freedom Linkages, Demonstrated up to 8-Bar J. Mechanisms Robotics. 2015;7(1):011006-011006-8. doi:10.1115/1.4029306 Double butterfly 8-bar adjacency matrix, graph, and linkage sketch Figure Legend:

3. Date of download: 7/10/2016 Copyright © ASME. All rights reserved. From: Automated Generation of Linkage Loop Equations for Planar One Degree-of-Freedom Linkages, Demonstrated up to 8-Bar J. Mechanisms Robotics. 2015;7(1):011006-011006-8. doi:10.1115/1.4029306 Example 8-bar adjacency matrix and adjacency graph Figure Legend:

4. Date of download: 7/10/2016 Copyright © ASME. All rights reserved. From: Automated Generation of Linkage Loop Equations for Planar One Degree-of-Freedom Linkages, Demonstrated up to 8-Bar J. Mechanisms Robotics. 2015;7(1):011006-011006-8. doi:10.1115/1.4029306 The first level shortest path Figure Legend:

5. Date of download: 7/10/2016 Copyright © ASME. All rights reserved. From: Automated Generation of Linkage Loop Equations for Planar One Degree-of-Freedom Linkages, Demonstrated up to 8-Bar J. Mechanisms Robotics. 2015;7(1):011006-011006-8. doi:10.1115/1.4029306 A second level shortest path Figure Legend:

6. Date of download: 7/10/2016 Copyright © ASME. All rights reserved. From: Automated Generation of Linkage Loop Equations for Planar One Degree-of-Freedom Linkages, Demonstrated up to 8-Bar J. Mechanisms Robotics. 2015;7(1):011006-011006-8. doi:10.1115/1.4029306 Two second level shortest paths Figure Legend:

7. Date of download: 7/10/2016 Copyright © ASME. All rights reserved. From: Automated Generation of Linkage Loop Equations for Planar One Degree-of-Freedom Linkages, Demonstrated up to 8-Bar J. Mechanisms Robotics. 2015;7(1):011006-011006-8. doi:10.1115/1.4029306 A third level shortest path Figure Legend:

8. Date of download: 7/10/2016 Copyright © ASME. All rights reserved. From: Automated Generation of Linkage Loop Equations for Planar One Degree-of-Freedom Linkages, Demonstrated up to 8-Bar J. Mechanisms Robotics. 2015;7(1):011006-011006-8. doi:10.1115/1.4029306 Another third level shortest path Figure Legend:

9. Date of download: 7/10/2016 Copyright © ASME. All rights reserved. From: Automated Generation of Linkage Loop Equations for Planar One Degree-of-Freedom Linkages, Demonstrated up to 8-Bar J. Mechanisms Robotics. 2015;7(1):011006-011006-8. doi:10.1115/1.4029306 The four unique cycles Figure Legend:

10. Date of download: 7/10/2016 Copyright © ASME. All rights reserved. From: Automated Generation of Linkage Loop Equations for Planar One Degree-of-Freedom Linkages, Demonstrated up to 8-Bar J. Mechanisms Robotics. 2015;7(1):011006-011006-8. doi:10.1115/1.4029306 The cycle basis Figure Legend:

11. Date of download: 7/10/2016 Copyright © ASME. All rights reserved. From: Automated Generation of Linkage Loop Equations for Planar One Degree-of-Freedom Linkages, Demonstrated up to 8-Bar J. Mechanisms Robotics. 2015;7(1):011006-011006-8. doi:10.1115/1.4029306 Double butterfly unique mechanisms Figure Legend:

12. Date of download: 7/10/2016 Copyright © ASME. All rights reserved. From: Automated Generation of Linkage Loop Equations for Planar One Degree-of-Freedom Linkages, Demonstrated up to 8-Bar J. Mechanisms Robotics. 2015;7(1):011006-011006-8. doi:10.1115/1.4029306 Double butterfly unique linkages Figure Legend:

13. Date of download: 7/10/2016 Copyright © ASME. All rights reserved. From: Automated Generation of Linkage Loop Equations for Planar One Degree-of-Freedom Linkages, Demonstrated up to 8-Bar J. Mechanisms Robotics. 2015;7(1):011006-011006-8. doi:10.1115/1.4029306 Naming convention, example 8-bar Figure Legend: