system: [SYSTEM]

user: 5. 结论 本文是在原来的基础上对HSSH机构进行分析和求解求出其末端运动学分析，通过利用切比雪夫多项式的逼近理论把正弦与余弦的复杂形势用简单的角度来分析，从而近似求解带有螺旋副的空间机构的运动学问题。这是对螺旋副的求解的一种新的想法，以达到抛砖引玉的目的。 图2. f(x) = cosπx与切比雪夫多项式在[−2，2]逼近图 图3. f(x) = sinπx与切比雪夫多项式在[−2，2]逼近图 Table 1 Position solution of spatial four-bar mechanism (HSSH) in the interval [−1，1] and the comparison of 序号 θ 1 /π 切比雪夫逼近的的l值 l的实际值 1 −2.23272 − 0.48755i 11.9458 + 8.949i 22.009 + 2.0535i 2 −2.23272 + 0.48755i 11.9458 − 8.949i 22.009 − 2.0535i 3 −2.1694 − 1.72387i 119.891 + 420.056i 109.436 + 26.94i 4 −2.1694 + 1.72387i 119.891 − 420.056i 109.436 − 26.94i 5 −1.2958 − 0.156198i 8.00047 − 0.00063366i 8.00118 − 0.0007169i 6 −1.2958 + 0.156198i 8.00047 + 0.00063366i 8.00118 + 0.0007169i 7 0.4670 8.0 8. 8 0.8988 8.0 8. 9 2.36383 − 0.326961i 14.632 + 32.0304i 9.519 + 5.6563i 10 2.36383 + 0.326961i 14.632 − 32.0304i 9.519 − 5.6563i 11 2.45352 − 1.62358i 484.942 + 827.467i 32.84 + 88.9414i 12 2.45352 + 1.62358i 484.942 − 827.467i 32.84 − 88.9414i 13 2.9176 805.87 9.2666 表1. 空间HSSH在区间[−1，1]的位置解及l的比较值 Table 2 Position solution of spatial four-bar mechanism (HSSH) in the interval [1，3] and the comparison of 序号 θ 1 /π − 2 切比雪夫逼近的的l值 l的实际值 1 −2.20723 − 0.48929i 8.03257 + 9.289i 20.4369 + 2.374i 2 −2.20723 + 0.48929i 8.03257 − 9.289i 20.4369 − 2.374i 3 −2.1679 − 1.723i 115.638 + 420.2i 108.997 + 27.05i 4 −2.1679 + 1.723i 115.638 − 420.2i 108.997 − 27.05i 5 −1.5309 7.9969 7.9720 6 −1.10 7.99999 7.99999 7 0.50104 8.0 8. 8 0.816849 8.0 8. 9 2.3728 − 0.387065i 29.9808 + 24.6736i 11. + 5.58105i 10 2.3728 + 0.387065i 29.980 − 24.6736i 11. − 5.58105i 11 2.4513 − 1.62352i 483.70 + 815.135i 33.05 + 88.4679i 12 2.4513 + 1.62352i 483.70 − 815.135i 33.05 − 88.4679i 13 2.9385 894.553 12.6541 表2. 空间HSSH在区间[1，3]的位置解及l的比较值 Table 3 Position solution of spatial four-bar mechanism (HSSH) in the interval [3，5] and the comparison of 序号 θ 1 /π − 4 切比雪夫逼近的的l值 l的实际值 1 −2.20089 − 0.48553i 7.85631 + 8.76975i 20.0353 + 2.1969i 2 −2.20089 + 0.48553i 7.85631 − 8.76975i 20.0353 − 2.1969i 3 −2.16738 − 1.72268i 113.715 + 418.617i 108.753 + 26.9293i 4 −2.16738 + 1.72268i 113.715 − 418.617i 108.753 − 26.9293i 5 −1.49719 7.54093 7.98165 6 −1.18316 6.99856 7.99989 7 0.641542 − 0.284941i 2.30551 + 1.56135i 8. + 2.35011 × 10 −7 i 8 0.641542 + 0.284941i 2.30551 − 1.56135i 8. − 2.35011 × 10 −7 i 9 2.39647 − 0.467088i 51.1451 + 6.96633i 13.5262 + 5.36307i 10 2.39647 + 0.467088i 51.1451 − 6.96633i 13.5262 − 5.36307i 11 2.44791 − 1.62442i 487.122 + 795.193i 33.5876 + 87.81i 12 2.44791 + 1.62442i 487.122 − 795.193i 33.5876 − 87.81i 13 2.96742 1032.15 17.0023 表3. 空间HSSH在区间[3，5]的位置解及l的比较值 Table 4 Position solution of spatial four-bar mechanism (HSSH) in the interval [−3，−1] and the comparison of 序号 θ 1 /π + 2 切比雪夫逼近的的l值 l的实际值 1 −2.27047 − 0.486029i 14.4796 + 9.8426i 24.5696 + 1.51286i 2 −2.27047 + 0.486029i 14.4796 − 9.8426i 24.5696 − 1.51286i 3 −2.17187 − 1.72393i 126.296 + 418.271i 110.073 + 26.5975i 4 −2.17187 + 1.72393i 126.296 − 418.271i 110.073 − 26.5975i 5 −1.28351 − 0.40428i 1.26928 − 8.01819i 7.99487 + 0.00163136i 6 −1.28351 + 0.40428i 1.26928 + 8.01819i 7.99487 − 0.00163136i 7 0.704136 − 0.156302i 6.18213 − 0.638802i 8. − 3.36612 × 10 −7 i 8 0.704136 + 0.156302i 6.18213 + 0.638802i 8. + 3.36612 × 10 −7 i 9 2.37274 − 0.319632i 13.824 + 34.1845i 9.35662 + 5.90112i 10 2.37274 + 0.319632i 13.824 − 34.1845i 9.35662 − 5.90112i 11 2.45438 − 1.62452i 490.71 + 831.978i 32.9637 + 89.2231i 12 2.45438 + 1.62452i 490.71 − 831.978i 32.9637 − 89.2231i 13 2.91156 781.677 8.17829 表4. 空间HSSH在区间[−3，−1]的位置解及l的比较值