## 1 Introduction  
Injection molding is a critical manufacturing process in modern industry. It is widely used in the automotive, electronic, medical, and consumer product industries. The mold clamping mechanism is a key subsystem that directly affects product quality, production efficiency, and operational safety. The mold clamping mechanism serves three main functions: (1) securely closing and aligning mold halves before injection, (2) maintaining sufficient clamping force during injection and packing to prevent flash and ensure dimensional accuracy, and (3) rapidly opening the mold for part ejection while minimizing acceleration during mold plate movement. Modern manufacturing environments create engineering challenges. Industries demand higher production speeds while requiring lower energy consumption, reduced maintenance costs, and extended equipment life. This creates a fundamental contradiction: high-speed operations typically result in higher acceleration forces, leading to increased vibration, mechanical stress, component wear, and shorter equipment life. Toggle mechanisms are widely used in industry because they can generate high clamping forces with relatively low driving power and excellent repeatability. These mechanisms require at least one toggle effect at the fully closed position, while double-toggle configurations provide higher clamping force and better operational safety. Many patents [1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12] serve as references for designing clamping mechanisms for injection molding machines, most of which belong to multiple-joint and Watt-chain mechanisms. [PERSON] et al. [13] pioneered genetic algorithm optimization for five-point double-toggle clamping mechanisms, establishing theoretical foundations for mechanism optimization while significantly reducing acceleration and driving force requirements. [PERSON] and [PERSON] [14; 15; 16] introduced innovative designs with dual dead-position configurations, achieving better motion characteristics and enhanced operational stability compared to traditional single dead-position designs. [PERSON] et al. [17] analyzed mechanical errors in nine-link double-toggle mechanisms through combined theoretical and experimental approaches. [PERSON] et al. [18] applied computational methods for in-depth studies of the clamping mechanism. [PERSON] et al. [19] developed comprehensive dynamic models considering inertia and deformation effects. [PERSON] and [PERSON] [20] used response surface methodology for geometric optimization of five-point systems. [PERSON] et al. [21] demonstrated that proper motion adjustment can reduce maximum mold acceleration fluctuations by over 50%. [PERSON] et al. [22] expanded applications to food packaging with electric eight-bar mechanisms. Despite extensive research on multiple-joint and Watt-chain mechanisms, exploration of alternative mechanisms remains relatively limited. Specifically, although Stephenson-I and Stephenson-II mechanisms are common in general kinematics literature, their feasibility and optimization for clamping system applications have not been systematically explored; the current literature lacks quantitative comparative studies between Stephenson-chain and optimized Watt-chain mechanisms; simultaneously, the potential of alternative mechanisms in reducing motion acceleration has not been thoroughly investigated, while acceleration directly affects machine vibration, component wear, and product quality. This study addresses these gaps through systematic optimization and comparative analysis of Stephenson-chain mold clamping mechanisms:  
1. Develop comprehensive kinematic models for Stephenson-I and Stephenson-II mechanisms with double-toggle effects. 2. Optimize both configurations for minimum acceleration and driving force through systematic parameter variation. 3. Perform quantitative comparative analysis against established optimal Watt-chain mechanisms under identical conditions.