1. Date of download: 10/11/2017
Copyright © ASME. All rights reserved.
From: Design and Validation of a Carbon-Fiber Collapsible Hinge for Space Applications: A Deployable Boom
J. Mechanisms Robotics. 2016;8(3): doi: /
Figure Legend:
(a) Representation of two tape-springs in parallel with the concave side facing each other. L is the length of the spring, RT is the internal radius of the tube, and M is the bending moment of the forces. (b) Boom in its deployed configuration where the deployment angle is 2θ=0. (c) Configuration of the stowed boom of length Lb (2θ=90 deg). The variable ms g is the weight of the sensor, and mb g is the weight of the boom.

2. Date of download: 10/11/2017
Copyright © ASME. All rights reserved.
From: Design and Validation of a Carbon-Fiber Collapsible Hinge for Space Applications: A Deployable Boom
J. Mechanisms Robotics. 2016;8(3): doi: /
Figure Legend:
(a) Reference frame of a single undeformed rib of a tape-spring. The x-axis points longitudinally, the y-axis transversally, and the z-axis points toward the center of the tube of radius RT. The thickness of the spring is h, and the subtended angle of the undeformed rib is 2α. (b) Deformation of the rib in opposite bending. Mx is the moment necessary to deform the spring. M− is the reaction moment generated by the spring under such deformation. Note that the centers of the longitudinal radius rL and transversal radius rT of the deformed spring are located at the opposite sides of the neutral plane of the rib and rL>0. (c) Deformed spring in equal bending.

3. Date of download: 10/11/2017
Copyright © ASME. All rights reserved.
From: Design and Validation of a Carbon-Fiber Collapsible Hinge for Space Applications: A Deployable Boom
J. Mechanisms Robotics. 2016;8(3): doi: /
Figure Legend:
(a) Orientation of force per unit measure on a spring sample and (b) orientation of moments per unit measure

4. Date of download: 10/11/2017
Copyright © ASME. All rights reserved.
From: Design and Validation of a Carbon-Fiber Collapsible Hinge for Space Applications: A Deployable Boom
J. Mechanisms Robotics. 2016;8(3): doi: /
Figure Legend:
Simplified example of force control in a redundant system. (a) Force is generated along the horizontal axis on a viscoelastic system. The arm configuration is redundant since only a monodirectional force can be generated by either kinetic or kinematic inputs of both the wrist and elbow joints. In this example, only the elbow is directly commanded using either the torque M or the angle θ. (b) Example of torque–angle curve at steady state when either elbow torque (black) or elbow joint displacement (gray) is used as input to command the force at the point of contact with the environment. It is apparent that the torque input produces instability in the neighborhood of the system's kinematic singularity (hand and forearm are almost on the same line). The different phases of the experiment are described in Sec. 3.1.

5. Date of download: 10/11/2017
Copyright © ASME. All rights reserved.
From: Design and Validation of a Carbon-Fiber Collapsible Hinge for Space Applications: A Deployable Boom
J. Mechanisms Robotics. 2016;8(3): doi: /
Figure Legend:
(a) Prebuckling longitudinal configuration of the spring and (b) postbuckling longitudinal configuration of the spring

6. Date of download: 10/11/2017
Copyright © ASME. All rights reserved.
From: Design and Validation of a Carbon-Fiber Collapsible Hinge for Space Applications: A Deployable Boom
J. Mechanisms Robotics. 2016;8(3): doi: /
Figure Legend:
Example of moment exerted by the spring as a function of the hinge rotation 2θ. All the solid lines are those followed by the real structure transitioning through flexural and torsional buckling. Dashed lines are theoretical conditions that are not achieved because of buckling transitions. Propagation moments during flexural buckling (a-b), flexural moment of nonbuckled structure (b-c and d-e-f), and torsional buckling caused by flexural moment in equal bending (a-c-d). The different transition phases are described in Sec. 4.

7. Date of download: 10/11/2017
Copyright © ASME. All rights reserved.
From: Design and Validation of a Carbon-Fiber Collapsible Hinge for Space Applications: A Deployable Boom
J. Mechanisms Robotics. 2016;8(3): doi: /
Figure Legend:
Buckling cycles of two springs in parallel where the gray spring is in equal bending and the black is in opposite bending. The diagram starts from the right and each step is described following the arrows counterclockwise.

8. Date of download: 10/11/2017
Copyright © ASME. All rights reserved.
From: Design and Validation of a Carbon-Fiber Collapsible Hinge for Space Applications: A Deployable Boom
J. Mechanisms Robotics. 2016;8(3): doi: /
Figure Legend:
(a) The accelerometer is glued on the top flange of the tube and (b) upper part of the tube with the top flange mounted, rotation of the boom occurs around the x-axis

9. Date of download: 10/11/2017
Copyright © ASME. All rights reserved.
From: Design and Validation of a Carbon-Fiber Collapsible Hinge for Space Applications: A Deployable Boom
J. Mechanisms Robotics. 2016;8(3): doi: /
Figure Legend:
(a) Simulated and experimental deployment angles. (b) Acceleration of the payload for the Z- and Y-axis of the payload as described in Fig. 8(a). The experimental measurements are calculated as the average of ten deployments. The shaded area represents one standard deviation. In both panels, the correspondence with the point in Fig. 7 is shown.

10. Date of download: 10/11/2017
Copyright © ASME. All rights reserved.
From: Design and Validation of a Carbon-Fiber Collapsible Hinge for Space Applications: A Deployable Boom
J. Mechanisms Robotics. 2016;8(3): doi: /
Figure Legend:
Moment versus angle of deployment. The first part of the deployment from a′ to b′ is dashed. The oscillation from d′ to e′ is dashed–dotted.

11. Date of download: 10/11/2017
Copyright © ASME. All rights reserved.
From: Design and Validation of a Carbon-Fiber Collapsible Hinge for Space Applications: A Deployable Boom
J. Mechanisms Robotics. 2016;8(3): doi: /
Figure Legend:
Spectrum of the acceleration along the y-axis of the accelerometer. Solid line corresponds to the direct measurement obtained with the experimental setup. Dashed line is the spectrum estimated using the simulation performed with simwise 4D. The two black vertical dashed lines indicate the first two frequency of the deployed boom.

12. Date of download: 10/11/2017
Copyright © ASME. All rights reserved.
From: Design and Validation of a Carbon-Fiber Collapsible Hinge for Space Applications: A Deployable Boom
J. Mechanisms Robotics. 2016;8(3): doi: /
Figure Legend:
Spectrum of the acceleration along the z-axis of the accelerometer. Solid line corresponds to the direct measurement obtained with the experimental setup. Dashed line is the spectrum estimated using the simulation performed with simwise 4D. The two black vertical dashed lines indicate the first two frequency of the deployed boom.