Compared to traditional three-pronged roller-type couplers, the three-pronged sliding universal coupling uses three sliding pin rods instead of three spherical or cylindrical rollers. This design allows it to transmit larger force moment. Additionally, its structure is simpler, and it comes with advantages such as easy installation, low manufacturing cost, and high transmission efficiency. It can be widely applied in situations requiring heavy torque and heavy loads. By using three sliding pin rods instead of three spherical or cylindrical rollers, the three-pronged sliding universal coupling improves upon the original three-pronged roller-type coupler, which suffered from high contact stress and significant wear due to small contact areas. This new type of three-pronged sliding universal coupling can be widely used in transmission systems, especially in the automotive industry, with broad prospects for application [12]. Therefore, conducting kinematic and dynamic performance analysis on it is of significant importance, paving the way for further applications in various fields. To achieve a precise analysis of the coupling, it is necessary to clearly define the composition of the coupling before conducting the relevant research. Based on this, we established the motion equations for the three-pronged universal coupling [13]. To understand the motion characteristics of universal couplings and further clarify the motion laws of this device, we designed an analysis method specifically for this device, focusing on the three-pronged universal coupling as the research object [14]. This article utilizes the direction cosine matrix to analyze the motion of the input and output shafts, studying the effects of the angle between the axes of the input and output shafts and the rotational frequency of the coupler on the motion of the sliding pin rod within the triple-rod sleeve holes. Building upon this motion analysis, the single force method is employed [15; 16; 17] to establish the force equilibrium equations for the output shaft and the input end shaft, followed by solving and analyzing these equations to delve into the dynamic behavior of the input and output shafts. In the dynamic analysis, the use of the single force method bypasses the need for complex solving processes. This method is a straightforward and intuitive approach to force analysis, where the focus lies not on simultaneously determining all constraint forces, but rather on initially calculating the constraint forces within a specific motion pair. Subsequently, the equilibrium equations for the remaining motion pairs are solved individually, component by component. The study of the three-pronged slip universal coupling was mainly carried out in the field of synchronicity and motion law. This research is mainly to establish a kinematic model and dynamic model that can guide the development of a new type of constant angular velocity universal coupling structure, and analyze the kinematics and dynamic characteristics of the new structure, which are of great significance to guide the application of a new type of three-pronged universal coupling. Most of the previous studies  
Figure 1: Tripod universal coupling assembly. 1—input shaft, 2—slide-rod, 3—coupling bearing, 4—tripod arm, 5—tripod. carried out by our group focused on the motion trajectory simulation of the components of the three-pronged sliding universal coupling (such as the center point slide bar, etc. ), but this study is to establish a guiding model and systematically analyze the model. In the introduction, the synchronization of the three-pronged sliding universal coupling was verified by the synchronization experiment under different rotation angles. The experimental results show that the universal coupling can achieve the effect of accurate angular velocity rotation.