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The flexible parallel mechanism is widely utilized in precision instruments, thanks to its numerous advantages, such as high precision, frictionless operation, and seamless movements. The establishment of the motion equations for this mechanism is crucial for designing, analyzing, controlling, and simulating parallel mechanisms. While the existing inverse kinematics solution theory is comprehensive, developing a forward solution model is challenging due to the nonlinear nature of the attitude equation. To address this issue, a new method based on the transfer matrix approach is proposed in this research to calculate the forward kinematics of parallel mechanisms. The proposed method is applied to analyze the forward kinematics and workspace of both planar and spatial flexible mechanisms. Simulation calculations and experiments are conducted to verify the method's effectiveness. The results demonstrate that the error is approximately 2%, indicating the feasibility and accuracy of the calculation method. [ABSTRACT FROM AUTHOR]

Lysine cyclodeaminase (LCD)-mediated synthesis of l-pipecolic acid (l-PA) from l-lysine (l-Lys) is a promising approach. However, only one LCD has been reported, and its inadequate activity limits industrial applications. To address this problem, a substrate analogue-guided enzyme mining strategy was employed. A novel ornithine cyclodeaminase (OCD) from Rhizobium leguminosarum ( Rl OCD) was identified in combination with directed macrogenomic approaches. Rl OCD displayed a conversion rate of 28% at a substrate loading as high as 1000 mM. A multiregion synergy strategy consisting of pocket reshaping, dynamical cross-correlation matrix-guided coevolutionary design, and surface modification was used to design Rl OCD from the inside-out. A quadruple mutant (V93C/L119C/I170T/R90L) designated Mu4 with significantly increased activity was obtained, which showed a 28.46-fold increase in the catalytic efficiency. The conversion of Mu4 was 91% within 10 h at 1000 mM (146.19 g L -1 ) loading. The space-time yield of 282.1 g L -1 d -1 is the highest level ever reported. Molecular dynamics simulations and interaction analyses revealed that efficient pocket expansion and unique conformational rearrangements increased the affinity for the substrate, resulting in a more catalytically active conformation. This study expands the toolbox for the production of l-PA and demonstrates the effectiveness and potential of Mu4 for its production.