Undergraduate Student Bucknell University Lewisburg, Pennsylvania, United States
Introduction:: Loss of finger mobility, specifically extension and flexion, is a common post-impairment caused by stroke (Lang CE, DeJong SL, et al). This disability brings difficulties in the patient’s daily life; furthermore, it requires endured rehabilitation to regain the movements which can become physically and mentally draining. Among recent developments in soft robotic rehabilitation devices, the negative stiffness of compliant shell mechanism, a thin-walled structure to achieve motion and force generation (Nijssen, J. P. A., Radaelli, et al), has been investigated as an alternative, yet not easy to create because of its instability (Brohuis). This mechanical property reflects the movement of a finger in which curling requires a minimum moment while extending requires a maximum moment in the same direction as the extension, referring to a negative stiffness spring. Driven by this impact to design a more efficient rehabilitation device, we develop a preliminary investigation of negative stiffness behavior in a compliant shell mechanism with a hyperbolic-parabolic shape, which has been tested for negative stiffness with a hypothesis to undergo a more prolonged and stable range (Brohuis), parametrized as
x= a*z2 - b*y2
In which z and y represent the longitudinal curvature and the transverse curvature respectively, while a and b determine the additions to the curvatures, creating different geometries. However, no specific geometry has been tested for negative stiffness. Hereby, through this research, the negative stiffness of different geometry and thickness of compliant shells is tested and analyzed using mechanical testing with the aid of computational programming.
Materials and Methods:: With computational modeling, optimization of the longitudinal and transverse sizes are found to be 60.325mm and 22.225mm respectively. Using ABAQUS analysis, different a and b values are utilized to model the movement of the compliant shell shape, giving results of the relative displacements in x, z, theta y (rotation). From this analysis, 5 pairs of a and b values (5 geometries) are predicted to make the compliant shells undergo negative stiffness (Table 1). These values of hyperbolic-parabolic shapes are then used to prototype the shells via a vacuum-forming process, using sheets of 0.3 mm and 0.5 mm PETG material (Figure 1). The shells are made with elongated flat ends as grips to use in testing. Those vacuum-formed shells then undergo testing with the SEIKA robot. One end of the shell is fixed to a base while the other one is clamped to the ATI 6-axis load cell attached to the robot arm (Figure 2). A trajectory is programmed for each a and b value hyperbolic-parabolic shell based on the x, theta y, and z displacement from ABAQUS analysis with a wait time of two seconds between each point on the path. This trajectory is executed by the robot while at the same time force/torque data is collected by the load cell and transferred to the computer before being analyzed using MATLAB. Each of the different geometry and thickness shells undergoes 4 trials of testing.
Results, Conclusions, and Discussions:: The load cell collects force and torque in all x, y, and z axes, yet, only force in the x-axis shows significant results. 4 out of 5 tested geometries with 2 different thicknesses undergo negative stiffness, defined by the region with a negative slope mostly at the beginning of the testing period from 0.0 mm to less than 11.0 mm displacement (Figure 3). However, the graduality of the negative stiffness varies greatly between each geometry and thickness. The compliant shell of a = 30 and b = 250 with a thickness of 0.3mm experiences the greatest change in the slope, indicating a steep range of negative stiffness. Yet, running a statistical t-test on MATLAB to compare the thickness effect on each geometry shows a significant difference between the two thicknesses except for a =36 b =300 shells in which the p-value is significantly smaller than 0.005 (Table 2). This overall trend of the shells undergoing negative stiffness matches the predicted analysis made by ABAQUS. In other words, a and b parameters, defining different geometries by adding curvatures to the longitudinal and transverse, contribute to the elongation of negative stiffness. This result agrees with Brohuis’ work on elongating the negative stiffness of compliant shells by increasing the longitudinal curvature of the hyperbolic-parabolic shape. Further comparison between the testing results and ABAQUS analysis can be achieved to better optimize the hyperbolic-parabolic parameter to accomplish the goal of elongating negative stiffness with higher stability. On the other hand, the effect of varying thicknesses in addition to geometries to elongate negative stiffness with more stability may require more tests with different variations of thicknesses. A higher range of thicknesses (larger than 0.2mm as done in the research) could bring significant results to evaluate. Moreover, during the testing process, noises from the execution of the robot are also captured in the load cell data; therefore, closer evaluation should be made to more accurately analyze the data. The shells, throughout the testing, introduce some behavior of yielding, which needs to be managed in a more efficient way to avoid affecting the final results.
Acknowledgements (Optional): : Professor Charles. A Kim, Professor of Mechanical Engineering, Bucknell University, PA
References (Optional): :
Broshuis, Ab. "Negative Stiffness in Compliant Shell Mechanisms: To develop a passive stroke rehabilitation device." (2019).
Lang, Catherine E et al. “Recovery of thumb and finger extension and its relation to grasp performance after stroke.” Journal of neurophysiology vol. 102,1 (2009): 451-9. doi:10.1152/jn.91310.2008
Nijssen, J. P. A., Radaelli, G., Kim, C. J., and Herder, J. L. (June 5, 2020). "Overview and Kinetostatic Characterization of Compliant Shell Mechanism Building Blocks." ASME. J. Mechanisms Robotics. December 2020; 12(6): 061009. https://doi.org/10.1115/1.4047344
