## 2 Materials and Methods  
Kinematic analysis serves as a foundational tool for characterizing the operation of a valvetrain. It enables preliminary calculations of loads and stresses while providing input data for engine thermal analysis. However, MBD analysis is critical to predict the vibrational behavior of the valve train, calculate dynamic loads and stresses, and identify potential component failures or contact losses, particularly at high engine speeds [10].  
MBD modeling assumes greater importance at elevated engine speeds, where inertial forces become substantial. Conversely, at lower speeds, such as during idle, the effects of dynamics are less pronounced, and kinematic models often yield reasonable approximations. Dynamic models also account for variables such as spring preload and residual cylinder pressure, which significantly influence valve movement and system loads, factors that are not directly addressed in kinematic analyzes.  
In essence, kinematic modeling provides a simplified representation of motion, whereas dynamic modeling offers a more comprehensive understanding of the interactions between forces and system behavior. Both approaches are integral to the thorough analysis of valve train performance, with dynamic modeling becoming increasingly essential under high-speed operating conditions.  
Kinematic modeling focuses on the analysis of motion, highlighting parameters such as displacement, velocity, and acceleration of components, including valves. Dynamic modeling, on the other hand, expands this scope by incorporating the forces that influence motion. Factors such as mass, stiffness, and damping are considered in dynamic models to facilitate an understanding of the vibrational behavior of the system. While kinematic models are relatively straightforward and provide an initial understanding of system motion, dynamic models are more intricate, accounting for the interactions of forces and their effects on component behavior.  
The FEV Virtual Dynamics 2019.1 software was used for kinematic and dynamic modeling and simulations in this study. This software, built on ADAMS, developed by Mechanical Dynamics, Incorporated (MDI) for the simulation of mechanical system motion in the time and frequency domain, utilizes ISO-certified processes to ensure precise equation formulation and reliable solution algorithms, validated through comparisons with published results and quality assurance standards [11]. It incorporates virtual prototyping into the engine development process, effectively bridging the gap between specialized industry tools and general-purpose simulation software [12]. This software combines engine-specific knowledge with a tailored interface and architecture, incorporating specialized elements such as push rods, gas forces, dynos, and valves, which can be refined to varying levels of detail depending on the development stage and data availability.  
The methodology of this study follows a four-stage process integrating kinematic modeling, dynamic simulation, experimental validation, and optimization. First, kinematic modeling is performed to define the cam profile, analyze displacement, velocity, and acceleration, and predict initial valve motion characteristics. Next, an MBD simulation is performed that incorporates mass, stiffness, damping, and external forces to analyze the interactions between valvetrain components, including contact forces and system vibrations. The definition types of the parts in the kinematic and dynamic models and their percentage distribution by mass are shown in Table 1. In the experimental validation phase, vibration accelerations are measured at multiple engine points and compared with simulation results to refine the model and ensure accuracy. Finally, the final optimization and validation stage involves adjusting key parameters such as spring stiffness, cam profile, and damping characteristics to improve valvetrain stability and performance. This integrated approach ensures a comprehensive analysis and validation of the proposed valvetrain design.