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Tham khảo tài liệu 'parallel manipulators towards new applications part 6', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 168 Parallel Manipulators Towards New Applications z-0.058 0.617 -0.558 0.010 0.557 -0.567 -0.678 0.289 0.390 -0.649 0.333 0.316 T _ -0.154 -0.154 -0.154 -0.230 -0.230 -0.230 Jg 0.905 -2.130 1.220 -0.103 2.520 -2.410 1.930 -0.181 -1.750 -2.840 1.330 1.510 -2.230 -2.230 -2.230 2.020 2.020 2.020 23 leg i ai bi Ui li qi 1 0.250 0.886 0.0 -0.126 0.180 0.2 0 0 1 1.25 1.221 2 -0.780 -0.421 0.0 -0.093 -0.199 0.2 0 0 1 1.25 1.221 3 0.755 -0.465 0.0 0.219 0.019 0.2 0 0 1 1.25 1.221 4 -0.250 0.886 0.0 0.115 0.164 0.4 0 0 1 1.70 1.933 5 -0.755 -0.465 0.0 -0.199 0.017 0.4 0 0 1 1.70 1.933 6 0.780 -0.421 0.0 0.085 -0.181 0.4 0 0 1 1.70 1.933 Table 1. Geometrical Parameters for the PKM Linapod at its home position. Fig. 9. Difference between discrete error calculation exact and linearization. Assuming that the length error for all bars is Ae 1 1 1 1 1 1 T with 10pm the total position error is AeEEF 11.528pm. This matches the exact solution using the nonlinear forward kinematics up to nine digits. In Fig. 9 the effect of variations of the scaling factor on Kinematic Modeling Linearization and First-Order Error Analysis 169 the difference Ae between linearized and exact model is illustrated. As it can be verified the approximation is accurate up to a geometric error of about e 1mm. Still for E 10mm the relative error is only about 1 which is still enough for most applications. This shows that the linearization procedure described in this paper is sufficient for most practical applications. 4.2 Accuracy of the Linapod In this section the geometric accuracy of the PKM Linapod is analyzed with the force-based method. Assuming errors in every component of the mechanism the sensitivity matrix Jg contains 126 columns corresponding to the individual geometric parameters. Orientation errors are ignored as these errors are negligible with respect to the translational errors. In Fig. 10 the overall error amplification index according to Eq. 16 is plotted over the workspace. It is recognized
