中文摘要：

提出了一种建立具有固定双面约束多点摩擦的多体系统动力学方程的方法．用笛卡尔坐标阵描述系统的位形，根据局部方法的递推关系建立系统的约束方程，应用第一类Lagrange方程建立该系统的动力学方程，使得具有摩擦的约束面的法向力与Lagrange乘子_对应，便于摩擦力的分析与计算，并用矩阵形式给出了摩擦力的广义力的一般表达式．应用增广法将微分-代数方程组转化为常微分方程组，并用分块矩阵的形式给出，以便于方程的编程与计算．给出了一种改进的试算法，可提高计算效率．最后给出了一个算例，应用试算法和RK法对算例进行了数值仿真．

英文摘要：

Modeling and simulating the dynamics of the multibody systems with bilateral constraints and dry friction are important in mechanical system and robotics. For smooth bilateral constraints, it is easy to solve the dynamical equations numerically. The dynamic equations of the multibody systems with the friction of constraint are the discontinuous differential-algebraic equations （DAE） and the equations cannot be expressed as being linear with respect to the generalized accelerations and the Lagrange multipliers directly. In the present paper, modeling of planar multi-rigid-body system with multi-friction and fixed-bilateral constraints is proposed. It is assumed that the system has sliding joints with Coulomb＇s dry friction and smooth hinge joints, while the sliding joints move along the fixed-slots. Firstly, the motion equations of the system are derived from Lagrange＇s equations of the first kind in Cartesian coordinate system, and constraint equations are expressed by local approach. A one-to-one map between the normal constraint forces and the Lagrange multipliers is established to analysis and compute the friction forces. Secondly, using the constraint equations and the principle of virtual work, the generalized forces of the friction forces are derived in the matrix form. The absolute value of Lagrange multiplier ｜λ｜ in the motion equations is given as λsgn（λ） by sign function. Therefore, the sign function, sgn（λ）, sgn（i） and sgn（s）, included in the motion equations, correspond to Lagrange multipliers, the velocity and tangential acceleration of the slider, respectively. Thirdly, the DAE are transformed into ordinary differential equations （ODE） by means of the augmentation approach. An improved trial-and-error method is proposed according to the characteristics of the piecewise smooth of the systems, which can improve the efficiency of computation. Finally, an example of one degree of freedom mechanism is given by improved triM-and-error method and R-K method.