## 2 Theory and Method  
The system framework of the coupling error compensation method is illustrated in Figure 1. This study first introduces the structural configuration and operational principle of the motion platform, followed by an analysis of the geometric error generation mechanism in the pitch and roll layers that significantly influence the table's positioning. Subsequently, coupling error modelling and compensation are implemented through the following methodology: initially establishing the kinematic model of pitch and roll layers then calibrating critical parameters in the kinematic model considering geometric errors. A coupling error model is developed based on rigid body motion assumptions, ultimately yielding the platform's error compensation model and position control strategy. The distribution characteristics, sensitivity indices, and variation patterns of geometric errors in the pitch and roll layers are systematically investigated through numerical simulations and compensation experiments. The experimental results validate the proposed coupling error compensation approach.  
As shown in Figure 2, the table's motion system is hydraulically driven to achieve a higher load capacity within a smaller volume. The motion axes, based on the assembly sequence, are categorized into the 1--longitudinal, 2--transverse, 3--rotary, 4--pitch, and 5--roll layers, each of which is rigidly connected and operates independently. The longitudinal and traversing layers are linear motion mechanisms consisting of hydraulic cylinders and guide rails. The rotary motion of the table is accomplished by the expansion and contraction of the hydraulic cylinders on both sides of the rotary level in opposite directions. The pitch and roll layers are both bilateral circular groove pulley mechanisms. The hydraulic cylinders on both sides of the mechanism will synchronously expand and contract to make the pulleys slide in the circular arc groove to achieve the rotation of the table. Inclination sensors are mounted on the table's flange to monitor changes in its attitude, while the hydraulic cylinders are fitted with internal displacement sensors to detect the actual stroke.  
Figure 1: Framework of coupling error compensation method.  
Figure 2: Composition of HLTST.  
The pose of the table is influenced by a multitude of error factors, which can be categorically grouped into four primary sources: geometric errors, control errors, force errors [26], and thermal errors [27]. Geometric errors are mainly caused by the machining, assembly, and fatigue wear of the parts, which are the principal factors that impact the motion accuracy of intricate mechanical systems [28].  
Figure 3 illustrates the internal architecture of the HLTST. The traverse layer and longitudinal layer both use precision guideways with high geometric and guiding accuracy, which have less influence on the table's pose. The rotary layer is assembled with high-precision shaft holes, which also have a low impact on the table's position. However, the pitch and roll layers, constructed with bilateral circular groove pulley mechanisms, present challenges due to their complex processing and assembly requirements. These result in significant geometric errors. Furthermore, the coupling nature of these structures means that movements in the pitch and roll layers can lead to cumulative coupling errors. In summary, this paper delves into the modelling and compensating of geometric errors in the pitch and roll layers, which influence the table's pose.