This dissertation performs a simulation investigation into the nonlinear static and dynamic characteristics of electrostatically driven shaped micro-actuators in micro-electro-mechanical systems (MEMS). The model proposed in the current nonlinear pull-in deflection study considers various boundary conditions for the electrostatically actuated structures, e.g. the cantilever beam and the fixed-fixed beam, and takes account of the electrical field fringing effect and the axial residual stress. Initially, the Adomian decomposition method is employed to evaluate the response of a micro-actuator incorporating a rectangular micro-beam and a flat electrode by obtaining the closed-form solution of the corresponding nonlinear equation. Since no iteration is required in solving the nonlinear deformation, this decomposition method is one of the most efficient methods available for evaluating the unstable pull-in behavior of an electrostatically driven micro-actuator. The present study implements both small and large deflection assumptions when simulating the response of the micro-actuator in order to explore the possible effects of the two models on the accuracy of the simulation results. The shaped micro-beam with a curved electrode micro-actuator is further assessed using the differential quadrature method (DQM) to examine the influence of the nonlinear pull-in effect. This dissertation also studies the contact force and the pull-in deflection of shaped micro-tweezers. The DQM is employed to solve the nonlinear interaction between the curved electrostatic field force and the corresponding deflection of the shaped cantilever actuators. The numerical results confirm the ability of the DQM to treat this form of nonlinear actuator problem accurately, efficiently and systematically. To evaluate the dynamic characteristics of the electrostatic micro-actuator, the DQM is applied to solve the natural frequencies of a fixed-fixed shaped beam vibrating around its statically deflected position under electrostatic loading. The proposed model not only takes account of the nonlinear interaction between the curved electrostatic field force and the restoring force of the shaped micro-beam, but also considers mid-plane stretching, axial residual stress, and electrical field fringing effects. It is shown that an excellent agreement exists between the simulation results obtained using the proposed model and those measured experimentally. This study also investigates the micro-beam and electrode shape effect on the natural frequencies of the actuator system. The analytical results indicate that variations in the shape of the micro-beam or of the electrode not only influence the electrostatic field distribution, but also significantly alter the dynamic characteristics of the micro-actuator. Furthermore, the results demonstrate that the shaped micro-beam with a curved electrode micro-actuator increases the working voltage range of the micro-actuator by a factor of approximately six times compared to that of a micro-actuator incorporating a rectangular micro-beam and a flat electrode. A continuing trend nowadays is the integration of micro-electro-mechanical devices with electronic circuitry to fabricate MEMS devices such as micro-switches, optical micro-mirrors, etc. It is known that when an electrical voltage is applied to these devices, the micro-actuators will undergo a residual vibration before reaching their permanent position. Hence, this dissertation investigates the residual vibration phenomenon of cantilever beam type micro-switches with air squeeze-film damping between the micro-beam and substrate. The present simulations of various shaped micro-actuators provide an understanding of the nonlinear static and dynamic behaviors of these devices and as such provide designers with the information required to properly and accurately control the device operating range during the design stage.

Recently, many industries pursue the goal of automatic high-speed assembly and manufacturing. So how to meet the requirement of high-precision and high-speed automatic assembly equipment is an important issue. In automatic assembly equipment, the inappropriate acceleration or deceleration motion will cause unsuitable inertia force and vibration to the positioning table. In order to reach the high production efficiency level, the problems of shortage of motor power, poor positioning accuracy, residual vibration, and noise shall be analyzed and solved. In previous researches, the researchers all devote to study acceleration and deceleration based on symmetrical time chart. In this paper, we change the accelerating and decelerating phase to reduce inertia force and decrease residual vibration of point-to-point motion. The system model is built to simulate dynamic response of the system. Through the results of simulation and experiment, we will discover the relations between the properties of motion and residual vibration about the high-speed positioning tables. It is expected to improve residual vibrations and design motion profiles according to those effective transient response control charts.

To provide point-to-point output motions needed for automation, intermittent indexing tables have widely been employed in various industries. For ensuring adequate production volume and profit margins, such devices are usually required to accurately generate intermittent motions as rapidly as possible. As a result, both of the positioning time and residual vibration are major concerns with the design of a fast, intermittent indexing table. A procedure that can be used to synthesize motor motion curves with minimized positioning time for intermittent indexing tables at high speeds is presented. First, based on the measured dynamic characteristic of an indexing table, it is then simulated to derive the equations of motion. Subsequently, favorable parameters for defining asymmetrical motor motion commands by S-curves for the modeled indexing table with improved kinematic and dynamic performance are identified. To verify the accuracy and effectiveness of the proposed approach, numerical and experimental results are revealed and compared to those obtained by using the traditional method.

Abstract The gear-cam intermittent mechanism, mainly made up by cam, the sun gear, planet gear and planetary shelf , it has been used in automatically high speed die cutting and creasing machine. The main function of die cutting and creasing machine is cutting and creasing the cardboard, and through compounding the cam motion curves, it will can control the intermittent motion of a gear-cam intermittent mechanism and improve its dynamic characteristic. The effects of gear cam profile and driving speed on the dynamic responses of a box folding and die cutting machine are studied in this work. The input driving motor¡Bgear¡Bgear-cam and output chain mechanics are included in the dynamic system. The equation of motion of the whole system in derived by employing Lagrange¡¦s equation the 4th order Runge-Kutta method is used to simulation the fine domain response of the nonlinear equation of motion. The effect of cam profile, and driving speed on the system dynamic response have been simulated and analysed in the work.

<p>Dynamic systems and robotic manipulators designed for time-optimal point-to-point motion are adversely affected by residual vibrations introduced due to the joint flexibility inherent in the system. Over the years, multiple techniques have been employed to improve the efficiency of such systems. While some techniques focus on increasing the system damping to efficiently dissipate the residual energy at the end of the move, several techniques achieve rapid repositioning by developing cleverly shaped input profiles that aim to reduce energy around the natural frequency to avoid exciting the resonant modes altogether. In this work, a numerical framework for constructing shaped inputs using a Versine basis function with peak acceleration constraint has been developed and improvements for the existing numerical framework for the Ramped Sinusoid basis function have been made to extend the range of values of the weighting function and improve the computational time. Performance metrics to evaluate the effectiveness of the numerical framework in minimizing residual vibrations have been developed. The effects of peak input acceleration and weighting function on the residual vibration in the system have been studied. The effectiveness of the method has been tested under multiple conditions in simulations and the results were validated by performing experiments on a two-link flexible joint robotic arm. The simulation and experimental results conclusively show that the inputs developed using the constrained numerical approach result in better residual vibration performance as compared to that of an unshaped input. </p>

During fast point-to-point motion, the inherent joint flexibility could be detrimental in terms of residual vibration. Aiming to minimize the vibration, the command shaping method has been developed so as to remove critical energy from the input profile at resonant frequencies. Since this method requires information of a physical model in order to find the target frequencies, the quality of the shaped command profile relies on the accuracy of the model parameter estimation. Therefore, in this work, a system identification method using Instrumental Variables is applied from the literature. Compared with the classic Ordinary Least Square method, the IV approach has successfully improved the estimation of parameters, based on simulation results. The accuracy of parameter estimation influences the command profile, as does the feedback controller. In this work, starting from a mathematical derivation with a mismatch model due to a feedback controller called Computed Torque Control, insight for the closed-loop system is given with regard to the interaction between control gains and the actual resonant frequencies. It is found that the control gain is able to modify the actual resonant frequency curve, and push it into or out of the shaping bounds which are generated from the command shaping method. Further analysis based on the simulation results shows that the overlap area between the shaping bounds and the actual frequencies affects the level of residual vibration. In light of this fact, an optimal control gain exists and is found when the estimation error is in a certain range. At the end, recommendations for choosing the control gains are provided.

The validity of transfer matrix method (TMM) employed in a nonlinear gear cam system is studied in this thesis. The nonlinear dynamic responses of each part in the nonlinear system are estimated by applying the 4th-order Runge-Kutta method. A high speed gear cam drive automatic die cutter was analyzed in this study. A 25 horsepower AC induction motor is designed to drive the system. To complete the cutting work, a sequential process of the harmonic motion and the intermittent motion are generated by the elbow mechanism and the gear cam mechanism, respectively. A simplified branched multi-rotor system is modeled to approximate the motion of the system. The variation of the dynamic parameters of the system in a loading cycle is estimated under a branched torsional system. The Holzer¡¦s transfer matrix method is used to study the variation of the system parameters during the intermittent movement. Moreover, the effect of time-varied speed introduced from the torque variation of the induction motor and gear cam mechanism on the nonlinear dynamic response of the system has also been investigated. To explore the dynamic effect of different cam designs, three different cam motion curves and seven operating rates have been analyzed in this work. The residual vibration of the last sprocket has also been discussed. Numerical results indicate that the proposed model is available to simulate the dynamic responses of a nonlinear gear cam drive system.