## 1 Introduction  
Turning is an essential functional skill for performing activities of daily living and maintaining mobility among persons after stroke [1] and older adults [2, 3]. Falling during turning is eight times more likely to result in hip fracture than falling while walking [4], which is due to landing on the hip while turning [5]. Stroke is associated with difficulty in turning [6], and this limited turning capacity increases the risk of falls. Although an association between risk of fall and turning is well known, minimal research exists about the execution of turning behavior comparing stroke and healthy controls. New insights into turning behavior or strategies will effectuate appropriate interventions for those after stroke. Previous studies have reported stroke survivors to take more steps and time while turning different angles (45\({}^{\circ}\), 90\({}^{\circ}\), and 180\({}^{\circ}\)) than did age-matched healthy individuals [6]. Specifically, turning among stroke survivors is compromised by either declined sensorimotor function [7] or slower self-paced movement speed [8]; however, comparative studies on kinematic analysis while turning among stroke survivors and healthy controls are lacking. [PERSON] et al. investigated turning in the Timed Up and Go (TUG) task with respect to spatiotemporal and kinematic parameters associated with stroke [9, 10], and few other studies reported turning phases using inertial sensors for 180\({}^{\circ}\) turning [11, 12]. [PERSON] et al. reported that movement speed, cadence, and step length were reduced onboth the paretic and non-paretic side among individuals after stroke during TUG. They also showed that single support phase, peak hip extension, knee flexion, and ankle dorsiflexion were significantly reduced on the paretic side among individuals after stroke compared to healthy counterparts during TUG [9, 10]. In contrast to TUG, our study defines turn cycle (TC) during 360\({}^{\circ}\) turning, similar to the concept of gait cycle during walking. This new turn cycle definition helps develop a methodology to assess turning ability and key turning characteristics using kinematic data in stroke survivors.  
Previous studies have focused on staggering (loss of balance), the number of steps taken to turn, time to turn, and type of turn (pivoting versus step turn) [3, 12, 13, 14]. We understand the importance of these turning parameters, but standardization of turning movement may provide a simple and easy strategy to compare turning among individuals. A 360\({}^{\circ}\) turn is critical to study since turning in TUG [15], and figure-of-eight [16] are affected by acceleration and deceleration occurring before and after the turn. The 360\({}^{\circ}\) turn times have been studied in community-dwelling older adults [17] and people with Parkinson's disease (PD) [18]. Some common activities of daily living such as toileting, showering, and other work activities in the kitchen may involve 360\({}^{\circ}\) turning. We investigated the 360\({}^{\circ}\) turn, which is critical since it is a quick, easy to perform test and suited for quick clinical assessments for stroke survivors. Contrastingly, other tests like TUG and figure-of-eight, where the body is required to reduce its momentum, rotate, and accelerate in a new direction are burdensome to stroke patients. This study aims to characterize patients' 360\({}^{\circ}\) turning ability utilizing kinematic data and assess new parameters of turning disability, which can identify the effectiveness of targeted rehabilitation of turning and possibly identify the severity of disease post-stroke.