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This paper presents a side-looking single-beam microwave vehicle detector (VD) system for estimation of per-vehicle speed and length. The proposed VD system is equipped with a 2-D range Doppler frequency-modulated continuous-wave (FMCW) radar using a squint angle. The associated Fourier processor uses an inverse synthetic aperture radar (ISAR) algorithm to extract range and speed data for each vehicle using a single-beam FMCW radar. The simulation and experimental results show accurate estimations of vehicle speed and length. The measurement errors of speed and length were approximately ±4 km/h and ±1 m, respectively. The proposed method has excellent detection capability for small moving targets, such as bikes and pedestrians, at speeds down to 5 km/h. A commercial 10.6-GHz radar with signal processing modifications was used in the experiments. IndexTerms-Frequency-modulated continuous wave (FMCW), intelligent transportation system (ITS), synthetic aperture radar (SAR), vehicle detector (VD). I. INTRODUCTIONV EHICLE detectors (VDs) are widely used to gather traffic information in an intelligent transportation system (ITS). The objective of a VD is to obtain traffic information, such as the speed and length of vehicles passing on a road. A wide range of sensor technologies are available for VDs, such as inductive loops, video, ultrasonic detectors, and microwave detectors. The advantage of radar-based detectors is that they are a mature technology because of past military applications. Radar-based detectors are unintrusive and can operate day or night in any weather conditions. A frequency-modulated continuous-wave (FMCW) radar is widely used for traffic data collection. It transmits a continuous-wave (CW) signal and compares the frequency difference between the transmitted and reflected signals to estimate the vehicle range and its speed.The installation methods of radar-based detectors can be classified as forward-looking and side-looking (or roadside). Forward-looking detectors have an illuminative direction parallel to the direction of traffic and are applied only to a single lane Manuscript

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Unlike a single universal joint, in which the output shaft rotates with a fluctuating speed depending on the misalignment angle, a double universal joint is used to connect two offset shafts. If a double universal joint is correctly arranged, with equal joint angles in perfect alignment, the output shaft rotates in a synchronous motion with uniform speed. However, in practice, the intermediate shaft of a double universal joint system suffers from bending moments induced by joint friction and velocity fluctuation induced by the joint angles. These factors distort the linear relationship between the input and output shafts. In this paper, the effects of joint angles and joint friction on the steady-state responses of a double universal joint system are examined. The mass matrix, damping matrix, stiffness matrix, and nonconservative force of a universal joint are derived analytically for finite element modeling. The formulation introduced generates an elementary matrix suitable for the analysis of complex rotor-bearing systems that include double universal joints.