Developing wearable platforms for unconstrained monitoring of limb movements has been an active recent topic of research due to potential applications such as clinical and athletic performance evaluation. However, practicality of these platforms might be affected by the dynamic and complexity of movements as well as characteristics of the surrounding environment. This paper addresses such issues by proposing a novel method for obtaining kinematic information of joints using a custom-designed wearable platform. The proposed method uses data from two gyroscopes and an array of textile stretch sensors to accurately track three-dimensional movements, including extension, flexion, and rotation, of a joint. More specifically, gyroscopes provide angular velocity data of two sides of a joint, while their relative orientation is estimated by a machine learning algorithm. An Unscented Kalman Filter (UKF) algorithm is applied to directly fuse angular velocity/relative orientation data and estimate the kinematic orientation of the joint. Experimental evaluations were carried out using data from 10 volunteers performing a series of predefined as well as unconstrained random three-dimensional trunk movements. Results show that the proposed sensor setup and the UKF-based data fusion algorithm can accurately estimate the orientation of the trunk relative to pelvis with an average error of less than 1.72 degrees in predefined movements and a comparable accuracy of 3.00 degrees in random movements. Moreover, the proposed platform is easy to setup, does not restrict body motion, and is not affected by environmental disturbances. This study is a further step towards developing user-friendly wearable sensor systems than can be readily used in indoor and outdoor settings without requiring bulky equipment or a tedious calibration phase.