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1、机器人学基础第西章机器人动力学THCh.4 Manipulator Dynamics6Ch.4 Manipulator Dynamics6Fundamentals of RoboticsChe4 Manipulator Dynamics中南大学蔡自兴，谢斌zxcai, 2010Ch.4 Manipulator Dynamics6Ch.4 Manipulator Dynamics6ContentsIntroduction to Dynamics Rigid Body DynamicsIffll Lagrangian Formulation0 Newton-Euler FormulationArt
2、iculated Multi-Body DynamicsCh4 Manipulator Dynamics IntroductionK7.P；=6gmx g人 h、= dx cos qxtential Energy P,K严孰盃Kinetic Energy K、apof link 14.1.1 Kinetic and Potential Energy of a Rigid BodyK, = g mdjOj + 壬 （ + 久）+ m2dd cos0、（Q； + p2 = _“gd cos q _ fn2gd2 cos（ q + g）4.1.1 Kinetic and Potential Ener
3、gy of a Rigid BodyKinetic and Potential Energy of a 2-hnks manipulatorg cos q、&2m,(d J2) 图4.2二连杆机器手(14.1 Dynamics of a Rijiid瓦孑$7?|J4.1 Dynamics of a Rigid Body124.1.1 Kinetic and Potential Energy of a Rigid Body Total Kinetic and Potential Energy ofa 2-links manipulator areK = K+K?=+ (/w, + rn2 )d0
4、 + 扌，叫+ Q 尸m2did2 cos &丄(Q： + Q0JP=PX+P2=一(“ + 4)gd cos! 一mgd2 cos(q +02)(4.4)Con tents4.1 Dynamics of a Rigid Bodv以 Introduction to DynamicsQ Rigid Body Dynamicsffll Lagrangian FormulationC3 Newton-Euler FormulationArticulated Multi-Body DynamicsCh.4 Manipulator Dy tunniesTH Lagrangian FormulationL
5、agrangian Function L of a2-links manipulator:l二 k 一 p=(/W| + 加2+ 加(Q； + 2&2 + Qj)+ m2dxd2 cosq(0： + Ofiy) + (加+ 叫)gd、cosq + m2d2 cos(q +O2)(4.5)4.1 Dynamics of a RiQd Body4.1 Dynamics of a RiQd Body虫匹一匹,i = ,2 dt dqi dqi4.1 Dynamics of a RiQd Body4.1 Dynamics of a RiQd BodyDynamic Equations:T -1 示西西
6、(4.6)d dL dLdt d02d02(4.7)0g 、S m(畑力)有效惯量(effective inertial)：关节，的加速度在关节i上产生的惯性力+!& A+02.21 +9A W&2 一_2I1)222 _2I2221 _如(4.10)J4.1 Dynamics of a Ri*id Body154.1.2 Two Solutions tor Dynamic Equationy Lagrangian Formulation4.1 Dynamics of a RiQd Body4.1.2 Two Solutions for Dynamic Equation Lagrangian Formulation Dynamic
