Design and Optimization of Contact-aided Compliant Mechanisms with Nonlinear Stiffness

Open Access
Tummala, Yashwanth
Graduate Program:
Mechanical Engineering
Doctor of Philosophy
Document Type:
Date of Defense:
September 30, 2013
Committee Members:
  • Mary I Frecker, Dissertation Advisor
  • George A Lesieutre, Committee Member
  • Matthew B Parkinson, Committee Member
  • Christopher Rahn, Committee Member
  • Design optimization
  • compliant mechanisms
  • passive morphing
  • ornithopters
  • contact-aided compliant mechanisms
Contact-aided compliant mechanisms are a class of compliant mechanisms where parts of the mechanism come into contact with one another to perform a specific task or to improve the performance of the mechanism itself. This dissertation presents design, optimization, and testing of novel, monolithic, contact-aided compliant mechanisms with nonlinear stiffness. They are called compliant spine, bend-and-sweep compliant element and twist compliant element. Such mechanisms have been designed to achieve passive wing morphing of flapping wing unmanned aerial vehicles or ornithopters thus improving their steady level flight performance. Ornithopters have a unique potential in revolutionizing both civil and military sectors. A compliant spine is a novel contact-aided compliant mechanism with nonlinear stiffness in the bending direction alone. Such a mechanism is very flexible when bent in one direction and is very stiff when bent in the other direction because of contact. This mechanism was designed to achieve passive bending of ornithopter wings during upstroke, while remaining fully extended and rigid during downstroke. The bend-and-sweep compliant element has nonlinear stiffness in two orthogonal directions, namely, bending and sweep directions. This mechanism was designed to achieve simultaneous passive bending and sweep of ornithopter wings during upstroke. During downstroke, this mechanism is very stiff in both bending and sweep directions because of contact, thus causing the wings to remain fully extended. Finally, twist compliant mechanism was designed to achieve passive twisting of ornithopters wings during upstroke. This mechanism is very flexible when twisted in the counter-clockwise direction but is very stiff when twisted in the clockwise direction because of contact between the parts of the mechanism. To design these contact-aided compliant mechanisms for ornithopter applications a new design optimization procedure was developed as part of this research. This procedure involves solving a multi-objective optimization problem using genetic algorithms with geometrical constraints. The objectives of the optimization problem were to minimize the mass and maximum von Mises stress while maximizing the deflections observed. The optimization problem was solved for compliant spine, bend-and-sweep compliant element and twist compliant element using numerical computing software, MATLAB and finite element software, ANSYS. The optimal solutions obtained from the optimization procedures were then fabricated and tested. Based on the optimization results for compliant spine and bend-and-sweep compliant elements, it was found that adding a compliant joint adds a small amount of mass but decreases their stiffness at the same time. The thickness of the optimal compliant hinges is dependent on the type of loads applied on the compliant elements. Based on the optimization results for twist compliant element, it was found that stiffness of a twist compliant element in its flexible direction is independent of the number of sectors while its stiffness in the stiff direction is dependent on the number of sectors and the thickness of the sectors. Testing of the compliant spine and bend-and-sweep compliant elements was done by our collaborators Ms. Aimy Wissa and Dr. James E. Hubbard Jr. at University of Maryland, College Park. Bench top testing of compliant spine showed that it results in a decrease in the power consumption of an ornithopter by 45% and increase its lift by 16%. Ornithopters with compliant spines were also successfully free flight tested at Air Force Research Lab - Wright Patterson Air Base indoor flight facility. Bench testing of the bend-and-sweep compliant element showed that simultaneous, passive bending and sweep of ornithopter wings is possible. The twist compliant element was tested for its nonlinear stiffness in the twisting direction. Finally, a mathematical model using rods and springs was developed to represent the leading edge spar of an ornithopter with bending compliant elements in it. Equations of motion for the mathematical model were derived using Newtonian mechanics and solved numerically. A shape matching optimization problem was formulated and solved to determine optimal locationsof bending compliant elements in the leading edge spar thus achieving shape tailoring of ornithopters wings during the whole flapping cycle.