The digital 6-DOF motion platform exhibits motion instability phenomena such as jitter or vibration impact during startup, reversal, and low-speed operation. This paper conducts a qualitative analysis from the perspectives of low-speed friction characteristics, structural features of digital servo stepping hydraulic cylinders, and the influence of different working states of the six sets of digital hydraulic cylinders on the platform's motion in parallel operation. The analysis shows that these factors are important contributors to the platform's motion instability. The analysis results help to propose targeted solutions in mechanical structure design, machining selection, and compensation strategies. 1 Introduction Hydraulic 6-DOF motion platforms are commonly used in large-scale motion simulators to achieve complex spatial motion. To date, most hydraulically driven 6-DOF motion platforms employ electro-hydraulic servo systems, consisting of high-precision electro-hydraulic servo valves and their servo amplifiers, servo cylinders, sensors, and digital-to-analog converters forming a closed-loop control system. While these systems offer fast response, high precision, and flexible control, they also suffer from sensitivity to oil contamination, complex debugging and maintenance, and the need for A/D and D/A conversion. Naval University of Engineering was the first in China to use digital servo stepping hydraulic cylinders (referred to as digital cylinders or digital hydraulic cylinders) in the hydraulic servo system of a 6-DOF motion platform, developing a digital 6-DOF motion platform. This platform replaces the complex electro-hydraulic servo closed-loop control system with a relatively simple (approximately open-loop control) digital hydraulic servo system, improving system stability and reducing the high requirements for hydraulic precision, while simplifying debugging and maintenance. However, the digital 6-DOF motion platform also has some problems in practical use, one of which is the phenomenon of unstable platform movement. This paper will provide a qualitative analysis of this issue. 2. Introduction to the Digital 6-DOF Motion Platform Similar to the structure of a parallel 6-DOF motion platform using an electro-hydraulic servo system, the digital 6-DOF motion platform consists of an upper platform, universal joints, digital cylinders, and a lower platform. The upper and lower platforms are connected by six sets of digital cylinders via upper and lower universal joints. Changing the extension and retraction lengths of the six sets of digital cylinders achieves the translation of the upper platform along the X, Y, and Z axes and its rotation around the X, Y, and Z axes. Because digital cylinders replace electro-hydraulic servo valves and servo cylinders, digital 6-DOF motion platforms differ significantly from parallel 6-DOF motion platforms using electro-hydraulic servo systems in terms of control system composition, control methods, and hydraulic power requirements. This difference stems primarily from the working principle of digital cylinders. Digital cylinders integrate analog-to-digital conversion, hydraulic amplification, and hydraulic actuators, generating position feedback within the cylinder. They directly receive digital pulse signals without the need for D/A or A/D conversion devices, directly controlling the cylinder's position and speed through digital pulses, achieving so-called endpoint target control. This simplifies complex closed-loop control (even multi-loop control) into a formally open-loop control, allowing users to focus on the control objective without having to expend excessive effort dealing with the numerous problems arising from closed-loop system control. This simplifies control links, significantly reduces system debugging and maintenance difficulty, and greatly reduces hydraulic oil precision requirements (reaching ISO 4406 18/15). 3. Analysis of Motion Instability In actual operation, the motion instability of the digital DOF motion platform is mainly manifested in the following ways: (1) Unstable start-up, i.e., when the platform starts moving from a stationary position, there is shaking or even slight impact; (2) Shaking and vibration during reversal, i.e., when the platform moves to certain special positions—when the digital cylinder reverses direction, the platform shakes or even vibrates, and the motion feels obviously unstable; (3) When the digital cylinder moves to certain positions in its stroke, the platform has slight vibration or crawling phenomena, etc. This reduces the simulation effect of the platform as a motion simulator to a certain extent and may damage the system components. We analyze the causes of motion instability from the following aspects. 3.1 Friction Characteristics During low-speed or reversing motion, friction in a position and speed servo system can cause low-speed jitter, reversing jitter, or even vibration and impact phenomena. The friction force in a hydraulic servo system is related to various factors, such as the structure of the hydraulic cylinder (motor), sealing method, lubrication method, load size, and movement speed, and exhibits a non-linear relationship. Friction is generally considered to include static friction, Coulomb friction, and viscous friction, and its influence on the system varies with the load, speed (including direction), structure, and lubrication method (boundary lubrication or liquid lubrication). Friction at low speeds is more complex, and many scholars have conducted theoretical and experimental studies on it, including mathematical descriptions and modeling of friction characteristics, and friction compensation. Friction models range from simple constant force models to complex models with seven parameters, considering static friction, negative viscosity, frictional memory, hysteresis, etc. Armstrong-Helouvry discussed these models. The LuGre model proposed by Can-udas et al. encompasses most friction characteristics, including static friction, Coulomb friction, and viscous friction, and even the so-called Stick-Slip friction in the Stribeck region, comprehensively reflecting the mechanism of friction. The mathematical expression of the LuGre model is as follows: Equations (1), (2), and (3) above can be combined into a friction equation to establish the force balance equation of the cylinder piston: Where: is the average Bristle deviation (m); is the piston speed (m/s); is the Coulomb friction force (N); is the maximum static friction force (N); is the total friction force (N); is the Bristles stiffness coefficient (N/m); is the Bristles damping coefficient (N/(m•s-1)); is the viscous friction coefficient (N/(m•s-1)); is the Stribeck speed (m/s); is a function describing the characteristics of partial static friction at constant speed. Stick-Slip friction is a comprehensive manifestation (function) of static friction, rising static friction, negative viscous slope, friction memory, and hysteresis, and is also an important reason for low-speed vibration. The physical description is roughly as follows: When in the Stribeck region (as shown by the dashed circle in Figure 1), the friction surface initially enters the static friction zone, requiring a large static friction force to initiate movement. However, once movement begins and the dynamic friction zone is entered, the friction force suddenly decreases. That is, the friction force exhibits a nonlinear negative slope change with increasing speed, causing a sudden change in the friction force value. For the hydraulic cylinder, this is equivalent to a nonlinear negative external load disturbance force being applied for a very short time, resulting in a so-called "jerky motion." To solve the Stick-Slip friction problem, some scholars have proposed measures such as observer-based adaptive friction compensation, neural network adaptive friction compensation, and general predictive control. The essence of these compensation or control measures is still the adjustment of control gain. For the Stribeck region and Stick-Slip friction in digital cylinder servo systems, the friction force can be regarded as a disturbance force load of the position closed-loop system. During startup (the process of speed from 0 to entering the viscous damping zone), low-speed operation, and reversing stages, when the cylinder is in boundary lubrication, the negative viscous slope (negative damping) characteristics of Stick-Slip friction cause phenomena such as jitter. However, unlike electro-hydraulic servo systems, digital cylinder servo systems possess internal mechanical position closed-loop feedback. Furthermore, the gain of this position closed-loop feedback system is not adjustable. This means that compensation and control strategies based on gain adjustment cannot be directly used, which is a challenge for friction compensation in digital cylinder servo systems. 3.2 Long-stroke valve-controlled asymmetric cylinder mechanism: The digital cylinders used in digital 6-DOF motion platforms are typical long-stroke (symmetrical) valve-controlled asymmetric cylinder mechanisms. Due to the structural asymmetry of asymmetric cylinders and the mismatch of symmetrical valve-controlled asymmetric cylinders, the flow gain, flow-pressure coefficient, and velocity gain differ in the forward and reverse motion directions, resulting in different dynamic and static performance in both directions. For valve-controlled asymmetric cylinder mechanisms, the compressibility of the oil in the cavity during reversal causes "squeezing" and "surging" of the oil, resulting in a huge pressure jump near the reversal point. When the external load is applied, if the effective working area ratio of the two chambers of the piston cylinder is less than 0.585 (where and are the effective working areas of the rodless and rod chambers, respectively), near the reversal point, the pressure jump in the rodless chamber may reach (oil supply pressure), while the pressure jump in the rod chamber may reach approximately . If equal to a constant, it will change the position of the pressure jump without changing the magnitude of the jump. Furthermore, due to structural asymmetry, the cylinder's forward and reverse speed characteristics differ before and after reversal. Discussing the difference in speed gain from a control perspective, when the total load is 0, the forward and reverse speed gain ratio is ; when the total load is not 0, the forward and reverse speed gain ratio is , where is defined as the forward load pressure and is defined as the reverse load pressure. This is only the ideal analysis result. The speed gain characteristics will also have irregularities that are difficult to describe: (1) Near the reversal point, the wear of the valve port throttling edge causes a decrease in speed gain; (2) Dead zone caused by Coulomb friction, dead zone caused by the small negative opening of the digital cylinder; (3) The clearance of the digital cylinder mechanical feedback mechanism - the large lead screw nut may cause local jumps in speed characteristics. From the analysis of speed gain, it can be seen that the cylinder's movement speed interacts with the load force on the cylinder, so a complex nonlinear relationship will be presented near the reversal point of the digital cylinder. 3.3 Inconsistency in the working state of each cylinder The overall pose control of the digital 6-DOF motion platform is also an open-loop control, while the linear displacement of the six sets of digital cylinders is an internal position closed-loop control of approximately open-loop control. The extension and retraction length of each cylinder is obtained in real time by the inverse motion solution of the platform to realize different poses of the upper platform. When the platform is in a certain position, the working states of each digital cylinder may be very different. For example, the magnitude, direction, and nature of the force (tension or compression) on the cylinder, the cylinder's movement speed, and the equivalent fluid volume of the two chambers of the valve-controlled cylinder (affecting the hydraulic stiffness of the valve-controlled cylinder), etc., may cause differences in the dynamic response characteristics (hydraulic natural frequency, damping ratio) of each cylinder. Figure 2 shows the change of the natural frequency of a long-stroke valve-controlled cylinder system of a 6-DOF motion platform over the stroke. Although this difference may not be significantly reflected in the motion stability during the large-scale movement of the platform, when the platform starts from a certain position or the cylinder reverses direction, slight differences in the response of each cylinder may be observed. Even worse, a cylinder may "move first" or "move later," which is reflected in the instability of the platform's motion through the parallel structure. In addition, the current digital 6-DOF motion platform uses a two-degree-of-freedom universal joint to connect each digital cylinder to the upper platform, instead of a three-degree-of-freedom ball joint. Therefore, the piston rod of the digital cylinder needs to rotate relative to the cylinder barrel to meet the platform's six-degree-of-freedom requirement. Due to the structural characteristics of the internal mechanical feedback of the digital cylinder, the rotation of the piston rod can cause positioning deviations in the digital cylinder. The rotation of each cylinder varies depending on the platform's posture (detailed research is still needed), and the resulting positional deviations will cause deviations in the overall platform posture, and even cause instability in the platform's motion. Moreover, the literature proposes that when the piston moves linearly within the cylinder while rotating relative to the cylinder, the two motions combine into a helical motion. When the rotational speed reaches a certain value, the combined large helical motion may change the stick-slip friction characteristics in the Stribeck region at low speeds in the hydraulic cylinder, and may even avoid the "negative viscous slope" of the Stribeck region, making the friction force and the piston speed present an ideal linear relationship. This is also a solution to improve the vibration and impact problems caused by friction. The literature studies methods to avoid stick-slip friction by actively controlling the piston rotation speed. Currently, there is no research on the impact of this property on digital cylinders, but the resulting changes and differences in the friction force near the reversal point or at low speeds in each cylinder may also be one of the reasons for the instability of the platform's motion under certain conditions. 4. Conclusion The factors causing motion instability in digital 6-DOF motion platforms are complex and may include machining accuracy, control strategies, and many other factors. This paper only provides a simple qualitative analysis from aspects such as friction, the structure of the digital cylinder, and its different working states in parallel platform motion. This has certain reference value for us to propose targeted control strategies, compensation schemes, or improve structural design, which helps to solve the problem of platform motion instability and thus improve the overall performance of digital 6-DOF motion platforms. (Proceedings of the 2nd Servo and Motion Control Forum, Proceedings of the 3rd Servo and Motion Control Forum)