In this dissertation, we have proposed a new dielectric elastomer actuator design and model that couples electrostatics, fluid mechanics, linear and nonlinear elastic deformations. The internal hydraulic pressure can amplify the structural deformation generated by induced electrostatic forces (Maxwell pressure), given the name of this class of actuators, hydraulically amplified dielectric elastomer actuators (HADEAs).

First, we developed novel lumped-parameter models (LPMs) using linear and hyper-elastic material models and second compared the LPM results with finite element analysis in quasi-static simulations. We analytically expressed the conditions for the snap-through instability in the HADEA, which appears after exceeding a certain voltage applied to the electrodes. We showed the Mooney-Rivlin LPM model is estimating the HADEA’s states more precisely compared to the linear material model, especially in the large actuation domain.

Next, we developed a dynamic LPM deriving the equations of motion using the Euler–Lagrange approach. The time-response and Lyapunov stability of the HADEA were studied for several cases. We included the effects of viscous losses in the actuator with a generalized non-conservative force in the equation of motion by considering pressure drops using the Reynolds equation for lubrication. The results showed that the effect of viscosity is significant, turning the nonlinear oscillatory systems into an over-damped-like system. The results of dynamic LPM were in qualitative agreement with finite element models.

Finally, we have designed and analyzed a stacked hydraulically amplified dielectric elastomer (SHADE) robot manipulator with considerable dexterity. We established the required coordinate transformations to determine the robot manipulator positions employing the piecewise constant curvature (PCC) assumption. The kinematic analysis that defines the position, velocity, and acceleration was presented in both recursive and matrix forms. Furthermore, we investigated the SHADE robot workspace using a modified Monte Carlo Algorithm.

We offered two methods for the inverse kinematic analysis of SHADE robot: Chain-Like Optimization with Embedded Controller Inverse Kinematic (CLOEC-IK), and Heuristic Optimization Inverse Kinematic (HO-IK). The CLOEC-IK approaches the SHADE robot as the connection of several rigid links and revolute joints and, it imposes geometrical constraints to solve an optimization problem with an embedded integral controller in a smooth-workspace. The HO-IK is established based on the heuristic optimization algorithm and the forward kinematic problem with several hard nonlinear constraints imposed by instabilities. We concluded that the CLOEC-IK method can provide an inverse kinematic solution with theoretically zero error in a smooth-workspace, while the application of HO-IK delivers better results in the actuators with hard nonlinearities and instabilities.

Degree Date


Document Type


Degree Name



Mechanical Engineering


Edmond Richer

Subject Area

Bioengineering and Biomedical Engineering, Electrical, Electronics Engineering, Mathematics, Applied, Mechanical Engineering, Physics

Number of Pages




Creative Commons License

Creative Commons Attribution-Noncommercial 4.0 License
This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 4.0 License.

Available for download on Friday, May 14, 2021