a bstract Tracking of the position of a moving object is an important engineering problem in many areas including military, industrial, medical, and consumer applications. This problem has been effectively solved with an Inertial Measurement Unit (IMU) that consists of three orthogonally placed accelerometers and gyroscopes. The resulting structure measures the linear acceleration and angular velocity of the mounting object in three dimensions. Knowing these parameters is enough to track the motion of the system with the help of additional mathematical operations. Micro Electro Mechanical Systems based vibratory rate gyroscopes are preferred in most emerging applications due to major reduction in fabrication cost, size and power consumption as well as, ease of integration with digital and electronic control systems compared to precise ring laser and fiber optic gyroscopes. These applications include robots navigation, GPS based navigation systems backup, smart airbags, anti lock braking systems, video camera picture stabilization, virtual reality headsets. Although these sensors initially fit for applications where cost and size are more important than performance, currently their performances satisfy and even surpass conventional sensing systems. In this dissertation, fundamentals of operation of the micromachined vibratory rate gyroscopes have explained with emphasis on dynamical relations, oscillation patterns, characteristics of gyroscope response to rotation rate induced coriolis force and phase relations. A gyroscope has been analyzed emphasizing on: a) suspension system analysis, b) analysis of damping mechanisms with the aim of optimizing structure design and c) electrical analysis including electrostatic drive and capacitive detection methods. Results from this analysis show the desired operation of micromechanical system.