Optical and magnetic encoders are widely used to measure joint angles. These sensors are required to be installed at the axes of rotation (joint centers). However, microelectromechanical system (MEMS) accelerometer and gyroscope-based joint angle measurement sensors possess the advantage of being flexible with regard to the point of installation. Inertial measurement units (IMUs) are capable of providing orientation and are also used for joint angle estimation. They conventionally fuse gyroscope and accelerometer data using Kalman filter-like algorithm to estimate the joint angles. This research presents a novel approach of measuring joint parameters—joint angles, angular velocities, and accelerations, of two links joined by revolute or universal joint. The gravity-invariant vestibular dynamic inclinometer (VDI) and planar VDI (pVDI) are used on each link to measure the joint parameters of links joined by revolute and universal joints, respectively. The VDI consists of two dual-axis accelerometers and an uniaxial gyroscope, while the pVDI consists of four strategically placed dual-axis accelerometers and a triaxial gyroscope. The measurements of joint parameters using the presented algorithms are independent of integration errors/drift, do not require knowledge of robot dynamics, and are computationally less burdensome.