1. Date of download: 6/21/2016 Copyright © ASME. All rights reserved. From: Closed-Form Solution for Constant-Orientation Workspace and Workspace-Based Design of Radially Symmetric Hexapod Robots J. Mechanisms Robotics. 2014;6(3):031007-031007-13. doi:10.1115/1.4026827 The Hexapod Robot model. (a) The model of a Hexapod Robot with virtual prismatic legs. (b) The model of a Hexapod Robot as three 2-RPR mechanisms. Figure Legend:

2. Date of download: 6/21/2016 Copyright © ASME. All rights reserved. From: Closed-Form Solution for Constant-Orientation Workspace and Workspace-Based Design of Radially Symmetric Hexapod Robots J. Mechanisms Robotics. 2014;6(3):031007-031007-13. doi:10.1115/1.4026827 The procedural flowchart for analytically determining the 3D COW of a hexapod robot Figure Legend:

3. Date of download: 6/21/2016 Copyright © ASME. All rights reserved. From: Closed-Form Solution for Constant-Orientation Workspace and Workspace-Based Design of Radially Symmetric Hexapod Robots J. Mechanisms Robotics. 2014;6(3):031007-031007-13. doi:10.1115/1.4026827 The model of a 2-RPR planar parallel mechanism. (a) A model of a 2-RPR planar parallel mechanism. (b) An example COW of a 2- RPR mechanism. Figure Legend:

4. Date of download: 6/21/2016 Copyright © ASME. All rights reserved. From: Closed-Form Solution for Constant-Orientation Workspace and Workspace-Based Design of Radially Symmetric Hexapod Robots J. Mechanisms Robotics. 2014;6(3):031007-031007-13. doi:10.1115/1.4026827 The COW is constrained by multiple circles Figure Legend:

5. Date of download: 6/21/2016 Copyright © ASME. All rights reserved. From: Closed-Form Solution for Constant-Orientation Workspace and Workspace-Based Design of Radially Symmetric Hexapod Robots J. Mechanisms Robotics. 2014;6(3):031007-031007-13. doi:10.1115/1.4026827 The 2-RPR mechanism with symmetric COW Figure Legend:

6. Date of download: 6/21/2016 Copyright © ASME. All rights reserved. From: Closed-Form Solution for Constant-Orientation Workspace and Workspace-Based Design of Radially Symmetric Hexapod Robots J. Mechanisms Robotics. 2014;6(3):031007-031007-13. doi:10.1115/1.4026827 The COW of a 2-RPR mechanism. (a) View of the 2D COW of a 2-RPR mechanism. (b) View of the 3D COW of a revolved 2-RPR mechanism. (c) Isometric view of the 3D COW of a revolved 2-RPR mechanism. Figure Legend:

7. Date of download: 6/21/2016 Copyright © ASME. All rights reserved. From: Closed-Form Solution for Constant-Orientation Workspace and Workspace-Based Design of Radially Symmetric Hexapod Robots J. Mechanisms Robotics. 2014;6(3):031007-031007-13. doi:10.1115/1.4026827 The top view of a radially symmetric hexapod robot Figure Legend:

8. Date of download: 6/21/2016 Copyright © ASME. All rights reserved. From: Closed-Form Solution for Constant-Orientation Workspace and Workspace-Based Design of Radially Symmetric Hexapod Robots J. Mechanisms Robotics. 2014;6(3):031007-031007-13. doi:10.1115/1.4026827 The top view of a radially symmetric hexapod robot with the three 2-RPR workspaces Figure Legend:

9. Date of download: 6/21/2016 Copyright © ASME. All rights reserved. From: Closed-Form Solution for Constant-Orientation Workspace and Workspace-Based Design of Radially Symmetric Hexapod Robots J. Mechanisms Robotics. 2014;6(3):031007-031007-13. doi:10.1115/1.4026827 The summation of the 3D 2-RPR mechanisms before and after the Boolean operation. (a) The union of the 3D COW of the 2-RPR mechanisms. (b) The intersection of the 3D COW of the 2-RPR mechanisms. (c) A top view comparing the intersection workspace with the union workspace. (d) A side view comparing the intersection workspace with the union workspace. Figure Legend:

10. Date of download: 6/21/2016 Copyright © ASME. All rights reserved. From: Closed-Form Solution for Constant-Orientation Workspace and Workspace-Based Design of Radially Symmetric Hexapod Robots J. Mechanisms Robotics. 2014;6(3):031007-031007-13. doi:10.1115/1.4026827 The symmetric workspace of a hexapod robot. (a) Top view of the union workspace with the intersection workspace overlayed. (b) Top view of the 3D COW workspace showing the upper surfaces and curves. (c) Perspective view of the 3D COW showing the points p t and p 0. Figure Legend:

11. Date of download: 6/21/2016 Copyright © ASME. All rights reserved. From: Closed-Form Solution for Constant-Orientation Workspace and Workspace-Based Design of Radially Symmetric Hexapod Robots J. Mechanisms Robotics. 2014;6(3):031007-031007-13. doi:10.1115/1.4026827 An optimized hexapod COW encapsulating the desired cylindrical workspace Figure Legend:

12. Date of download: 6/21/2016 Copyright © ASME. All rights reserved. From: Closed-Form Solution for Constant-Orientation Workspace and Workspace-Based Design of Radially Symmetric Hexapod Robots J. Mechanisms Robotics. 2014;6(3):031007-031007-13. doi:10.1115/1.4026827 The lateral COW of the hexapod robot covering the desired workspace Figure Legend:

13. Date of download: 6/21/2016 Copyright © ASME. All rights reserved. From: Closed-Form Solution for Constant-Orientation Workspace and Workspace-Based Design of Radially Symmetric Hexapod Robots J. Mechanisms Robotics. 2014;6(3):031007-031007-13. doi:10.1115/1.4026827 The procedural flowchart for determining the optimal structures of hexapod robot for a desired workspace Figure Legend:

14. Date of download: 6/21/2016 Copyright © ASME. All rights reserved. From: Closed-Form Solution for Constant-Orientation Workspace and Workspace-Based Design of Radially Symmetric Hexapod Robots J. Mechanisms Robotics. 2014;6(3):031007-031007-13. doi:10.1115/1.4026827 Visualization of the desired cylindrical workspace within the 3D COW of the optimized hexapod robot Figure Legend:

15. Date of download: 6/21/2016 Copyright © ASME. All rights reserved. From: Closed-Form Solution for Constant-Orientation Workspace and Workspace-Based Design of Radially Symmetric Hexapod Robots J. Mechanisms Robotics. 2014;6(3):031007-031007-13. doi:10.1115/1.4026827 A maximized 3D COW of a hexapod robot within a desired cylindrical workspace Figure Legend:

16. Date of download: 6/21/2016 Copyright © ASME. All rights reserved. From: Closed-Form Solution for Constant-Orientation Workspace and Workspace-Based Design of Radially Symmetric Hexapod Robots J. Mechanisms Robotics. 2014;6(3):031007-031007-13. doi:10.1115/1.4026827 Maximizing the workspace of hexapod robot Figure Legend: