Wearable inertial measurement units (IMUs) are a cheaper alternative to video motion capture systems and can measure human movement in any environment. However, the state estimation methods used to convert noisy IMU data into joint kinematic data typically require numerical integration, resulting in significant integration drift. This study presents a novel integration-free nonlinear optimization method for measuring human movement with IMUs. The method utilizes a physics-based kinematic model with joint constraints to provide theoretical relationships between IMU kinematics and joint kinematics and replaces numerical integration with differentiation. It does not require IMU magnetometer data, calculation of IMU orientation in the global reference frame from IMU gyroscope data, or subtraction of the acceleration due to gravity from IMU accelerometer data. The method was evaluated quantitatively using experimental IMU and video motion capture data collected from the pelvis and lower limbs of a healthy subject who performed walking, jogging, and jumping trials. The proposed integration-free optimization method produced average root-mean-square (RMS) errors on the order of 3 deg for walking, 6 deg for jogging, and 12 deg for jumping. With a machine learning enhancement, these errors were reduced to roughly 3 deg for all three movements. In contrast, a standard unscented filter method produced average RMS errors of 18 deg, 19 deg, and 16 deg for the same three movements, respectively. These findings suggest that the proposed integration-free optimization method for estimating joint kinematics from IMU data could potentially be used in place of a video motion capture system for patient assessment when real-time measurement capability is not required.