Static balance is the reduction or elimination of the actuating effort in quasi-static motion of a mechanical system by adding non-dissipative force interactions to the system. In recent years, there is increasing recognition that static balancing of elastic forces in compliant mechanisms leads to increased efficiency as well as good force feedback characteristics. The development of insightful and pragmatic design methods for statically balanced compliant mechanisms is the motivation for this work. In our approach, we focus on a class of compliant mechanisms that can be approximated as spring-loaded rigid-link mechanisms. Instead of developing static balancing techniques directly for the compliant mechanisms, we seek analytical balancing techniques for the simplified spring–loaded rigid–link approximations. Towards that, we first provide new static balancing techniques for a spring-loaded four-bar linkage. We also find relations between static balancing parameters of the cognates of a four-bar linkage. Later, we develop a new perfect static balancing method for a general n-degree-of-freedom revolute and spherical jointed rigid-body linkages. This general method distinguishes itself from the known techniques in the following respects: 1 It adds only springs and not any auxiliary bodies. 2 It is applicable to linkage shaving any number of links connected in any manner. 3 It is applicable to both constant(i.e., gravity type) and linear spring loads. 4 It works both in planar and spatial cases. This analytical method is applied on the approximated compliant mechanisms as well. Expectedly, the compliant mechanisms would only be approximately balanced. We study the effectiveness of this approximate balance through simulations and a prototype. The analytical static balancing technique for rigid-body linkages and the study of its application to approximated compliant mechanisms are among the main contributions of this thesis.

This work develops and examines design strategies for reducing the stiffness of 3D-printed compliant mechanisms. The three aspects of a flexure that determine its stiffness are well known: material, boundary conditions, and geometry. In a highly constrained design space however, flexure stiffness may remain unacceptably high even while arriving at the limits of design constraints. In this work, changes to geometry and boundary conditions are examined that lead to drastically reduced stiffness behavior without changing flexure thickness, width, or length. Changes to geometry can result in very complex mechanisms. However, 3D printing enables almost arbitrarily complex geometries. This dissertation presents three design strategies for stiffness reduction: static balancing, lattice flexures, and compound joints. Static balancing refers to changes in the boundary conditions that result in a near-zero net change in potential energy storage over the useful deflection of a flexure. In this work, I present a method for static balancing that utilizes non-dimensional parameters to quickly synthesize a joint design with stiffness reduced by nearly 90%. This method is not only simple and straightforward, it is applicable to a wide range of flexure topologies. The only requirements on the joint to be balanced are that it must be approximated as a pin joint and torsion spring, and it must have a well-understood stiffness when subjected to a compressive load. Lattice flexures result from modifications to geometry that reduce cross-sectional area without changing width or thickness. However, the reduction in stiffness is greater than the reduction in cross sectional area. This can occur because the bending load is now carried by beams partially in torsion. Two lattice geometries are proposed and analyzed in detail using analytic and numeric techniques. It is shown that the off-axis stiffness behavior of lattice flexures can be better than that of conventional blade flexures while bending stiffness is reduced >60%. Compound joints are those that consist of arrays of flexures arranged co-axially. This arrangement provides increased range of motion, generally decreased stiffness, and improved stability. Additionally, a method is herein presented to reduce the parasitic center shift of a compound joint to nearly zero at a specified deflection. The penultimate chapter demonstrates how all three strategies can be used together, and includes new results to facilitate their combination.

Haptic interfaces are robotic force-feedback devices that give the user a sense of touch as they interact with virtual or remote environments. These interfaces act as input devices, mapping the 3-dimensional (3D) motions of the user's hand into 3D motions in a slave system or simulated virtual world. A major challenge in haptic interfaces is ensuring that the user's experience is a realistic depiction of the simulated environment. This requires the interface's design to be such that it does not hinder the user's ability to feel the forces present in the environment. This "transparency" is achieved by minimizing the device's physical properties (e.g., weight, inertia, friction). The primary objective of the work is to utilize compliant mechanisms as a means to improve transparency of a haptic interface. This thesis presents work toward the design of a fully compliant mechanism that can be utilized in haptic interfaces as a means to reduce parasitic forces. The approach taken in this work is to design a series of mechanisms that when combined act as a statically balanced compliant joint (SBCJ). Simulated and experimental results show that the methods presented here result in a joint that displays a significant decrease in return-to-home behavior typically observed in compliant mechanisms. This reduction in the torque needed to displace the joint and the absence of friction suggest that the joint design is conducive to the methods previously proposed for increasing transparency in haptic interfaces.

Robotics and space applications represent areas where compliant mechanisms can continue to make a significant impact by reducing costs and weight while improving performance. Because of the nature of these applications, a common need is for bearing replacement mechanisms, or mechanisms that perform the function of a bearing without the complexity and failure modes associated with bearings. Static balancing is a design strategy that attempts to reduce the actuation effort of a mechanism, and has been applied to compliant mechanisms in some applications. Monolithic construction, especially by means of 3D printing technology, is a strategy whereby the mechanism links and joints are built as a single "chunk" of material. This eliminates assembly and failure modes associated with wear and friction in traditional joints. In this work we examine these design strategies in the context of robotics and space applications. Matlab and Ansys batch files can be found in Appendix A. A fully compliant zero-torque, statically balanced mechanism is described that can undergo greater than 100 of motion. Because compliant mechanisms achieve their motion from the deflection of their constituent members, there is some strain energy associated with actuated positions. By introducing an appropriate pre-load, strain energy can be held constant. This can reduce or nearly eliminate the input force required from the actuating device. This paper describes the statically balanced rotary joint concept, and demonstrates its optimization, testing, and implementation for a haptic pantograph mechanism. The statically balanced properties of the constituent joints result in a mechanism with two balanced degrees of freedom. Matlab and Ansys batch files can be found in Appendix B. The conception, modeling, and development of a fully compliant two-degree-of-freedom pointing mechanism for application in spacecraft thruster, antenna, or solar array systems is described. The design objectives and the advantages of a compliant solution are briefly discussed. A single design concept is selected for final development from a field of generated concepts. Analytical and numerical models are accompanied by prototype testing and measurements in several iterations. A final design is described in detail, a fully compliant prototype is fabricated in titanium, and its performance is measured.

The balancing of a wind turbine rotor is a crucial step affecting the machine’s performance, reliability, and safety, as it directly impacts the dynamic loads on the entire structure. A rotor can be balanced either statically or dynamically. A method of rotor balancing was developed that achieves both the simplicity of static balancing and the accuracy of dynamic balancing. This method is best suited, but not limited, to hollow composite blades of any size. The method starts by quantifying the mass and center of gravity of each blade. A dynamic calculation is performed to determine the theoretical shaking force on the rotor shaft at the design operating speed. This force is converted to a net counterbalance mass required for each blade. Despite the most careful methodology, there may still be large errors associated with these measurements and calculations. Therefore, this new method includes a physical verification of each blade’s individual balance against all other blades on the rotor, with the ability to quantify the discrepancy between blades, and make all balance adjustments in situ. The balance weights are aluminum plugs of varying lengths inserted into the root of each blade with a threaded steel rod running through the middle. The balance adjustment is thus not visible from outside. The weight of the plug and rod represent the coarse counterbalance of each blade, based on the dynamic calculations. The threaded steel rod acts as a fine adjustment on the blades’ mass moment when traveled along the plug. A dedicated blade-balance apparatus, designed and constructed in-house, is used to verify and fine-tune each individual blade and compare it to all other blades on the rotor. The resulting blade assembly is verified on a full rotor static balancing apparatus. The full rotor apparatus measures the steady state tilt of the rotor when balanced on a point. Next, the rotors' tilt is related to its overall level of imbalance with quantifiable error. Most error comes from the fact that the hub, comparable in mass to the blades, creates a false righting moment of the assembly not present in operation. The fully assembled rotor is tested, pre and post balance, in operation on the turbine at a series of predetermined speeds. This is accomplished with a 3-axis accelerometer mounted on the main turbine shaft bearing and a control system which regulates and records turbine speed at 100 Hz