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Abstract
As a key component in mechanical transmission, the disc cam mechanism transforms the continuous motion of the active element into the complex, desired motion of the driven element through a specific profile curve. This study deeply analyzes the operating principles and structural types of the disc cam mechanism and elaborates on its profile design methods, covering theoretical formula derivation and computer-aided design methods, validated by practical examples. Furthermore, the current status and development trends of its applications in various fields, such as automotive, aerospace, and automation equipment, are explored. This provides theoretical support and practical guidance for the optimized design and widespread application of disc cam mechanisms, thereby meeting the demands of modern mechanical systems for high-precision, high-reliability, and efficient transmission.

I. Introduction
In modern mechanical systems, achieving precise and diverse motion transmission and control is crucial. Disc cam mechanisms, with their unique advantages, play a central role in numerous mechanical devices. By cleverly designing the cam profile curve, the driven element can be made to move according to a predetermined pattern, such as precisely controlling valve opening and closing in engine valve trains and accurately conveying and positioning materials in automated production lines. As the manufacturing industry moves toward high speed, precision, and intelligence, the performance requirements for disc cam mechanisms are becoming increasingly stringent. In-depth research on their design and application is of great practical significance.

II. Operating Principle and Structural Types of Disc Cam Mechanisms
2.1 Operating Principle
A disc cam mechanism primarily consists of a cam, a follower, and a frame. The cam, as the active element, typically rotates at a constant velocity, and the shape of its profile determines the motion of the follower. As the cam rotates, the profile contacts the follower, converting the cam's rotational motion into linear reciprocating motion or oscillating motion of the follower through high-pair contact. During this process, the radial changes at each point on the cam profile correspond to different displacements, velocities, and accelerations of the follower, achieving precise conversion of motion forms and parameters.

2.2 Structural Types
2.2.1 Classification by Cam Shape
Disc cam: The most common type, disc-shaped, with the cam profile lying in a plane perpendicular to the axis of rotation. Its simple structure allows for widespread application, particularly in applications with small follower travel, such as the thread take-up mechanism of a sewing machine. Cylindrical cam: The cam is cylindrical, with the profile curve located on the cylindrical surface. Special design of the cylindrical surface curve enables more complex follower motion. It is often used in mechanisms requiring high spatial motion, such as the feed mechanism of automatic machine tools.

Conical cam: The cam is conical, with the profile curve located on the conical surface. It can achieve a certain degree of spatial motion transmission and is useful in specific mechanical devices, such as the motion control mechanism of some textile machinery.

2.2.2 Classification by Follower Type
Tip follower: A simple structure accurately implements the motion pattern specified by the cam profile, but the tip is susceptible to wear and is only suitable for applications with low force transmission and low speed, such as micro-motion mechanisms in instrumentation.

Roller follower: A roller is installed at the end of the follower, converting point contact into line contact, reducing wear and allowing it to withstand large loads. It is widely used, such as in the rocker arm mechanism of an automobile engine. Flat-bottomed follower: The follower's flat end reduces contact stress when in contact with the cam profile. Under certain conditions, the direction of the force between the cam and follower remains constant, improving transmission efficiency. It is often used in high-speed cam mechanisms, such as the valve train in internal combustion engines.

III. Disc Cam Profile Design Methods
3.1 Theoretical Design Methods
3.1.1 Principle of the Reversal Method
The basic method for disc cam profile design is the reversal method. Assume that a common angular velocity equal to and opposite to the cam's rotational velocity is applied to the entire cam mechanism. In this case, the cam will be stationary, while the follower, while rotating around the cam axis at an angular velocity along its guide, also performs reciprocating linear motion or oscillation relative to the guide according to a given motion law. Based on this relative motion relationship, the coordinates of the follower's tip or roller center at various locations can be calculated in the fixed cam coordinate system, thereby obtaining the cam profile.

3.2 Computer-Aided Design (CAD) Methods
With the advancement of computer technology, CAD has become widely used in disc cam profile design. Using professional mechanical design software such as AutoCAD, SolidWorks, and Pro/E, cam profile design can be completed efficiently and accurately. Using SolidWorks as an example, the design process is as follows:

Establish a mathematical model: Based on the motion of the follower, input relevant parameters into the software, such as the cam base circle radius, roller radius, travel distance, and travel time, to construct a mathematical model of the cam profile.

Sketch: Use the software's drawing tools to sketch the cam profile based on the mathematical model and preliminarily determine the curve shape.

Parametric design: Parameterize the sketch, linking the input parameters to the sketch's geometry, ensuring automatic sketch updates when parameters are modified.

Motion simulation analysis: In the software's motion simulation module, add kinematic constraints between the cam and follower, set motion parameters, and perform motion simulation. By observing changes in parameters such as the follower's motion trajectory, velocity, and acceleration, verify the design's rationality and adjust parameters to optimize any inconsistencies.

IV. Application Examples of Disc Cam Mechanisms in Various Fields
4.1 Automotive Engine Valvetrain
In automotive engines, disc cam mechanisms are used to control valve opening and closing. For example, in a four-stroke gasoline engine, both the intake and exhaust cams are disc cams. Precisely designed cam profiles ensure that the intake and exhaust valves open and close at the appropriate times, ensuring optimal intake and exhaust performance, and improving combustion efficiency and power performance. According to statistics, optimized valve cam mechanisms can improve engine fuel economy by 5%-8% and power output by 10%-15%. At high engine speeds, the precisely designed cam profile ensures rapid and smooth valve opening and closing, reducing gas flow resistance and engine power loss.

4.2 Automated Packaging Machinery
In automated packaging machinery, disc cam mechanisms are often used to control operations such as packaging material conveying, product filling, and sealing. For example, in a granular packaging machine, a disc cam mechanism controls the intermittent motion of the conveyor belt, enabling precise filling and packaging of materials. The cam profile is designed based on the packaging process flow and operating rhythm, ensuring that the conveyor belt remains stationary during material filling and quickly moves to the next station after filling. This ensures a smooth and impact-free movement throughout the entire process, improving packaging efficiency and quality. In actual production, this packaging machine, driven by a disc cam mechanism, can achieve a packaging speed of 60-80 packages per minute, with minimal packaging error, effectively improving production efficiency and reducing costs.

4.3 Aircraft Engine Fuel Injection System
Aviation engines require extremely high precision in fuel injection control, and the disc cam mechanism plays a vital role in this process. In the fuel injection system of a certain aircraft engine, the disc cam mechanism controls the injection timing and amount of fuel from the injectors. By designing a complex and precise cam profile and taking into account the fuel injection requirements of different engine operating conditions (such as takeoff, cruise, and landing), the injection process is precisely controlled, ensuring stable and efficient engine operation under various operating conditions. Experiments have shown that fuel injection systems using advanced disc cam control can reduce aircraft engine fuel consumption by 3%-5% and increase thrust by 8%-12%, significantly improving engine performance and reliability and providing a strong guarantee for safe flight.

V. Development Trends in Disc Cam Mechanisms
5.1 High-Precision and High-Reliability Design
With the increasing demands for product quality and performance in modern manufacturing, disc cam mechanisms must exhibit even higher precision and reliability. In design, more advanced mathematical models and optimization algorithms are employed to consider the impact of multiple factors, such as material properties, manufacturing tolerances, and workload, on the cam profile curve, enabling precise design. Furthermore, high-precision manufacturing processes and testing methods, such as five-axis CNC machining and laser measurement technology, are employed to ensure cam manufacturing accuracy, reduce wear and deformation during operation, and improve the reliability and service life of the mechanism.

5.2 Lightweight and Energy-Saving Design
Against the backdrop of energy shortages and increasingly stringent environmental requirements, disc cam mechanisms are developing towards lightweight and energy-saving designs. The use of high-strength, low-density materials, such as aluminum alloy and titanium alloy, for cam and follower components reduces mechanism weight, reduces inertia, and improves energy efficiency. Furthermore, by optimizing the cam profile, friction loss and impact loads during movement are reduced, further contributing to energy conservation. Lightweight disc cam mechanisms are increasingly being used in mechanical components related to new energy vehicles, effectively reducing overall vehicle energy consumption.

5.3 Intelligent and Flexible Design
To meet the demands of smart manufacturing and personalized production, disc cam mechanisms will incorporate intelligent and flexible design concepts. By integrating intelligent components such as sensors and controllers, the mechanism's operating status can be monitored in real time, and motion parameters can be automatically adjusted based on changing operating conditions, achieving intelligent control. Furthermore, a modular design approach enables disc cam mechanisms to quickly adapt to the demands of different products and production processes, providing greater flexibility and improving the flexibility and adaptability of production systems. For example, in automated production lines in smart factories, disc cam mechanism parameters can be quickly adjusted based on changes in product orders, enabling efficient production of diverse products.

VI. Conclusion
Disc cam mechanisms, with their unique motion conversion capabilities, are widely used in numerous fields. Through research on its operating principles, structural types, profile design methods, and case studies across multiple fields, it is clear that the rational design of disc cam mechanisms is crucial for improving the performance of mechanical equipment. With technological advancements, disc cam mechanisms will continue to develop in terms of high precision, high reliability, lightweighting, energy saving, intelligence, and flexibility, continuously meeting the increasing demands of modern manufacturing for mechanical transmission and control, and providing strong support for technological innovation and development across various industries. In the future, further strengthening of basic theoretical research, combined with advanced technologies, will be necessary to promote the innovative application and performance breakthroughs of disc cam mechanisms in more fields.