A comparison of contact forces between the constrained gripper and the under-constrained gripper to grip the same work-piece is analyzed. The new type heavy forging grippers with constrained rods are designed to improve the contact status. The main difference between the new grippers with constrained tongs and the traditional grippers with under-constrained tongs is that the constrained gripper has constrained rods to keep the two tongs parallel. A gripping model has been presented in which the gripping operation is equivalent to the grasp of multi-fingered robot hands with friction contact point model. The models for calculating contact forces with constrained tongs and under-constrained tongs are presented with different constraint functions based on gradient flow optimization algorithms, and the constraint functions describe the definite state of the tongs during forging operation. By comparing the simulation and experiment results of the contact and gripping forces, it shows that the contact forces are different when the gripping in different rotation angles and the contact forces with constrained tongs is much smaller than that with under-constrained tongs, especially in the vertical position
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