Based on these requirements, we propose a mechanism to support eyelid closure, which we call the eyelid gating mechanism (ELGM). This mechanism transforms simple rotational actuation to three-dimensional and complex motion through deformation of soft material. This mechanism can use rigid actuators like a rotational motor as a power source, thus it can provide responsive and robust movement. Moreover, the end effector attached to the eyelid is made of soft material, thus the mechanism can provide good affinity and does not cause overload or strain on the eye.
Design rule of ELGM
The current ELGM design is shown in Fig. 3. This ELGM is composed of a support part, two handle parts, and a fixed base. The support part is made of soft material, and the nob part can hook to the eyelid. The handle parts are made of a rigid material and each of them has a hinged end. These hinged ends are fixed on an eyeglass-type frame crossing its rotational axes of hinged ends. These hinged ends must be located in the tail and inner corners of the eye, respectively. This mechanism was designed in SolidWorks and printed using VeloClear (rigid material) and Agilus 30 (soft material) on an Objet500 Connex2 3D printer (Stratasys Ltd.). In this case, the shore hardness of support part is A50. These support and handle parts were printed as a single piece.
This ELGM was designed following the design rules shown in Fig. 4. Figure 4a shows the design parameters for the support and handle parts. L is the distance between both hinged ends. The curved line of the support part is based on a precise circle. The handle parts are placed on the extension of the centerline of the circle. Its inclination is \(\psi\), and its length is l. The red line shows the initial ELGM posture, which corresponds to the opening phase of the eyelid. The blue line shows the deformed ELGM posture corresponding to the eyelid closure phase. The parameter H corresponds to the width between the upper and lower eyelids, which is determined by L, l, and \(\psi\). Figure 4b shows the fixation parameters. \(\phi\) shows the angle between the rotation axes on the handle parts, \(L'\) shows the distance between the fixed positions of each hinged end, and \(\theta\) shows the input deformation value.
In this study, we set the value of each parameter in Fig. 4 based on an article which reported the anthropometry of Asian eyelids [13]. According to this article, the width between the upper and lower eyelids is 7.5 mm to 9.0 mm, and the width between the rail and inner corners of the eye is 20 mm to 30 mm. Based on these values, we set the value of each parameter to be 9 mm < H < 10 mm, L = 42 mm, and \(\psi = 40^{\circ }\).
Deformation analysis of the ELGM
We conducted deformation analysis using the parameters l, \(\phi\), and \(L'\) as variables. We used non-liner finite element analysis from ANSYS inc. We defined the ELGM material to be a hyperelastic material in the simulation, which is similar to the ELGM material properties. We calculated the deformation at each rotational input angle \(\theta\) under forced displacement. We defined the contact position between the handle and fixation parts as frictionless. All other contact positions were bond. The number of ELGM nodes was approximately 2000.
The calculation results are shown in Figs. 5 and 6. Figure 5 shows an overview of the deformation analysis results, where each colored line is related to the red line in Fig. 3, and the black line shows the locus of the black dot in Fig. 3. We extracted the deformation loci along the Y-Z direction, which are shown as black lines in Fig. 5 with respect to each parameter. The extracted results are indicated as a − 1, b − 1, and c − 1 in Fig. 6. We also calculated the curvature of these loci with a least-squares approach with respect to each parameter, which are indicated as a − 2, b − 2, and c − 2 in Fig. 6. Moreover, we measured the maximum deformation along the Y direction for each parameter, and the results are indicated as a − 3, b − 3, and c3 in Fig. 6.
In terms of the handle length l, a longer handle length contributes to less deformation along the Y direction, and the curvature has a local maximum when l is approximately 5 mm. For the fixation angle \(\phi\), a larger fixation angle contributes to larger curvature during deformation and does not affect deformation in the Y direction. Shorter fixation distance \(L'\) between the handle parts transfers the circular arc deformation along the Y direction. From the nature of this mechanism, the fixation parts must be placed closer to the face than the nob attach to the eyelid, and it is more difficult to attach the nob to the eyelid when deformation in the Y direction is larger. The fixation parts and the ELGM deformation loci must be closer in order to maintain contact with the eyelid. In this case, from the results of this deformation analysis and exploratory prototyping, we prepare a prototype with l = 5 mm, \(\phi\) = 50°, and \(L'\) = 38 mm for use in the following experiments.