# A Kinematic Model of the Shoulder Complex Obtained from a Wearable Detection System
## 1 Introduction  
In recent years, the population with upper limb physical disabilities caused by stroke and other diseases has increased rapidly with the aggravation of social aging and improvement in living standards. To repair upper limb motor dysfunction, the application of advanced robot technology is becoming increasingly popular [1; 2; 3]. Due to the complex coupled motion of the shoulder mechanism [4; 5], the design of the guiding movement rules of rehabilitation robots generally lacks specific motion coupling information between the glenohumeral (GH) joint center and humeral elevation angle [6; 7; 8]. To obtain a kinematic model of the shoulder complex, it is necessary to understand the movements of the shoulder joints [4; 5; 6]. Because the shoulder complex is a very complicated and correlative system, many researchers have simplified the shoulder complex to a combination of the GH joint and the shoulder girdle [5; 6; 7; 8]. Generally, the GH joint has three revolute degrees of freedom (DOFs) with axes intersecting perpendicularly in the GH joint center, which is obviously a spherical joint [9; 10; 11; 12; 13; 14]. The shoulder girdle has been considered as a serial mechanism (a 2-DOF universal joint [11], twoprismatic joints [12], a combination of a 2-DOF universal joint and a 1-DOF prismatic joint [7; 8], a combination of a 3-DOF spherical joint and a 1-DOF prismatic joint [13], and a combination of a 3-DOF spherical joint and a 2-DOF universal joint [14]) or a closed-loop mechanism ([PERSON] model [15], [PERSON] model [16], [PERSON] model [17], [PERSON] model [18], and dynamic model [19; 20]). Although establishing the shoulder mechanism model is the basis of quantitatively describing the movement of shoulder complex during humeral elevation, it is not sufficient to only consider the mechanism model when obtaining the kinematic model of the shoulder complex. The joint coupling motion relationship between the GH joint and the shoulder girdle during humeral elevation as well as the differences in different elevation planes should also be considered [8; 12; 14; 21; 22; 23]. For the invisibility of the GH joint and shoulder girdle, obtaining kinematic information is very difficult. Some researchers have studied the exact coupling motion relationship of the shoulder complex using a pin inserted into the sternum, clavicle, scapula and humerus, grouping the results as the \"gold standard\" by collecting data to analyze the coupling relationship [22]. Other researchers have studied the specific exact motion coupling relationship using X-ray and computed tomography [23; 24]. Unfortunately, the motion coupling relationship of the shoulder complex is for a particular position [7; 8]. For daily rehabilitation training, there is no need to acquire accurate detection for each of the joint-coupled motions of the shoulder complex. The precision requirements of human daily movement science can be met by using motion capture technology based on skin markers to acquire the GH joint and shoulder girdle motion data [8; 21]. However, considering the complexity of the shoulder complex and the convenience of the experiment, only a few researchers have applied this technique to obtain the relative different elevation angles and elevation planes by estimating the instantaneous rotation center of the GH joint through the average position of three marker points at each time [7; 8; 21; 25]. With the development of sensor measurement technology, it is becoming increasingly popular to acquire human motion information based on sensor units or detection devices [2; 3], which have the characteristics of low cost, easy integration, and convenient detection [26].