地日运动的C^1R^2P^2机构重演及其应用于向日计算  

Earth-Sun Movement Recapitulation with C~1R~2P~2 Mechanism and Its Calculation Applied in Heliotropism

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作  者:张威[1,2] 许晓峰[3] 王立文 ZHANG Wei;XU Xiaofeng;WANG Liwen;Airport College,Civil Aviation University of China;Aviation Ground Special Equipment Research Base;Aeronautical Automation College,Civil Aviation University of China;

机构地区:[1]中国民航大学机场学院,天津300300 [2]中国民航航空地面特种设备研究基地,天津300300 [3]中国民航大学航空自动化学院,天津300300

出  处:《机床与液压》2016年第5期166-170,188共6页Machine Tool & Hydraulics

基  金:国家自然科学基金委员会与中国民航局联合资助项目(U1233106);中央高校基本科研业务费专项资金资助项目(ZXH2012H007);中国民航大学校级科研项目(2012KYE05)

摘  要:通过将自由系统等效变换为非自由系统的思想,可以利用机构学方法实现天文运动关系的可视化表达。提出一套假想C^1R^2P^2串联机构作为地日运动的相当系统,以5个运动副(1个圆柱副,2个转动副和2个移动副)来耦合地球对日运动。通过对黄赤交角和黄道椭圆轨道等约束条件的满足,该机构可重演地球任意点的对日运动。同时,利用D-H参数法,在机构的运动空间中建立了日心和地球位点的时间-空间方程。把此方程应用到太阳定向上,推导出由时间及经纬度表出的太阳方向公式。将Michalsky算法中太阳高度角和方位角计算公式以及王炳忠太阳赤纬计算公式作为参考,给出传统太阳矢量公式。最后通过3个实例,将得出的两组太阳方向向量进行对比,并计算出对应的误差。结果表明:该机构和由机构正向运动学导出的太阳方向公式是正确的。此外,对地日运动的更高精度修正,可通过调整或增加运动副来层次化重演。该研究方法可为天文运动学研究提供一种形象手段,以更好地理解运动关系。Through the idea of equivalently transforming a free system into a constraint system,theory of mechanism can be applied to realize visualization of astronomical movement relations.An imaginary C~1R~2P~2 serial mechanism was proposed to be an equivalent system of earth-sun movement system.In which,five kinematic pairs( one cylindrical pair,two rotation pairs and two movement pairs) were used to couple the earth-sun movement.The meahanism was reproduced movement of any earth's location around sun by satisfying astronomy constraints such as obliquity of the ecliptic,elliptic orbit,and etc.Meanwhile,Denavit-Hartenberg parametric method was used to establish time-space equation of earth's location to sun's center in kinematic space of the presented mechanism.The equation was applied into solar orientation,and an expression of solar direction vector by time,longitude and latitude was derivated from it.A traditional solar direction calculation was given with solar elevation angle and azimuth in Michalsky algorithm and WANG'ssolar declination formula.Finally,three examples were supplied to compare two groups of equations of solar direction,and corresponding errors were calculated.The results show that the presented mechanism and the derivated forward kinematics solar direction equation are correct.Moreover,a higher precision correction of earth-sun movement can be hierarchically reproduced by adjusting or increasing movement pairs.The methodology provides a figurative means for study of astronomical kinematics,so as to better understand relationship of movement.

关 键 词:地日运动 太阳定向 机构学 正向运动学 D-H参数法 

分 类 号:TH112.1[机械工程—机械设计及理论] P128.1[天文地球—天体测量;天文地球—天文学]

 

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