Abstract: General formulations for design sensitivity analysis of multibody system dynamics governed by ordinary differential equations with general objective functions in integral forms are obtained through the adjoint variable method.It is more efficient at computation than the direct differential method in the case of many design parameters,because there is no need to compute a huge amount of derivatives of generalized coordinates with respect to the design parameters.In order to improve computation speed and accuracy,the integral type of objective function and its derivatives with respect to the design parameters are transformed into simple ordinary differential equations.A numerical example of a planar manipulator model with two links is presented in the end.