## 1 Introduction
### Kinematic Analysis of the Spatial RRURR Electric Releasing Mechanism
Using the kinematic solution of the serial single-loop mechanism, the angle of joint \(R_{\text{I+1}}\) can be obtained as a function of the angle of joint \(R_{A}\), i.e., \(\theta_{\text{I+1}}=f(\theta_{A})\), thereby realizing motion transmission and driving transference. Then, joint \(R_{\text{I+1}}\) can be regarded as a virtual drive of the inverted sub-chain 2;
4. Using the transmission performance index through Formula (6), the motion/force transmission performance index of sub-chains 1 and 2 can be solved separately. The overall motion/force transmission performance index of the single-loop mechanism is constructed as the product of the input motion/force transmission performance indices of sub-chains 1 and 2. 1.2 Calculation Procedure for Solving the Overall Motion/Force Transmission Performance Index of a Single-Loop Mechanism  
Based on the kinematic model in Figure 7, the calculation procedure for the overall motion/force transmission performance index of the single-loop RRURR electric opening mechanism is shown as follows:  
1. Split the single-loop mechanism into a parallel mechanism with two sub-chains and select the middle link, \(CC^{\prime}\), of the U joint, (\(SOC\left\{-\overbrace{R_{C}\bot R_{C^{\prime}}}^{\text{2}}-\right\}\)), as the moving platform. 2. Calculate for the input motion screw and motion screw of each joint axis and the corresponding transmission-force screw in sub-chain 1 containing the input drive, \(R_{A}\). Solve the input motion/force transmission performance index of sub-chain 1: \[\gamma_{I_{1}}=\frac{\left|\$_{\$_{T_{1}}}\circ\$_{I_{1}}\right|}{\left|\$_{ \$_{T_{1}}}\circ\$_{I_{1}}\right|_{max}}\] where \(\$_{I_{1}}\) is the input motion screw of sub-chain 1, \(\$_{T_{1}}\) is the transmission-force screw of sub-chain 1, and \(\left|\$_{\$_{T_{1}}}\circ\$_{I_{1}}\right|\) represents instantaneous power.
3. The motion/force is transmitted along sub-chain 1 and the moving platform to joint \(R_{C^{\prime}}\). Invert the mechanism, and the moving/fixed platforms convert. Regard joint \(R_{C^{\prime}}\) as the input drive of inverted sub-chain 2. The angle of joint \(R_{C^{\prime}}\) is a function of the angle of joint \(R_{A}\), which can be obtained through kinematics solutions (5) of the mechanism. Similarly, the input motion screw, motion screw of each joint axis, and corresponding transmission-force screw in the inverted sub-chain 2 are calculated and the input motion/force transmission performance index of the inverted sub-chain 2 is solved: \[\gamma_{I_{2}}=\frac{\left|\$_{\$_{T_{2}}}\circ\$_{I_{2}}\right|}{\left|\$_{ \$_{T_{2}}}\circ\$_{I_{2}}\right|_{max}}\]
4. The overall motion/force transmission performance index is constructed as the product of the input motion/force transmission indices of sub-chain 1 and inverted sub-chain 2: \[\gamma=\gamma_{I_{1}}\cdot\gamma_{I_{2}}\] (7) where \(\gamma_{I_{1}}\) and \(\gamma_{I_{2}}\) are directed, which transmits motion/force from the input joint to output joint through chain-driving transference and the moving/fixed platform inversion. \(\gamma\in[0,\,1]\); the larger \(\gamma\) is, the better the overall motion/force transmission performance of the single-loop mechanism is.  
Motion/Force Transmission Performance Analysis of a Single-Degree-of-Freedom Single-Loop Spatial RRURR Mechanism  
When the vehicle side-door latch performs electric releasing, the mechanism operates at a fast speed and with great sealing-reaction force, which places high demands on the mo tion/force transmission performance of the chain. Therefore, it is necessary to analyze the motion/force transmission performance of the electric releasing RRURR overconstrained mechanism. The steps are as follows:  
1. For a single-loop RRURR mechanism, point C with a definite translational motion along the x-axis is selected as the moving platform. The chain, \(SOC\{-R_{A}\|R_{B}\|R_{C}-\}\) containing the input motion screw, is regarded as sub-chain 1, where \(\$_{A}\) is the input motion screw. \(SOC\{-R_{E}\|R_{D}\|R_{C}-\}\) is regarded as sub-chain 2.