Dynamic Modelling Of Planar Flexible Multiple-Link Manipulators

• Published in: International journal of modelling & simulation 1997-01, Vol.17 (2), p.151-159
• Main Authors: Hwang, S.-T., Broberg, H.L., Guo, R.-M.
• Format: Article
• Language: English
• Subjects: Applied sciences; Computer science; control theory; systems; Control theory. Systems; Exact sciences and technology; flexible manipulators; Lagrange-Euler formula; Robotics; Transformation matrix; vibration modes
• ISSN: 0228-6203; 1925-7082
• DOI: 10.1080/02286203.1997.11760324

This paper models and simulates a multiple-link planar flexible manipulator with only rotary joints in a vector-matrix form, which is suitable for control and optimization studies. The proposed method has no limitation on the number of links. In order to incorporate the effect of the link deflection, two coordinate systems are assigned at each end of each link. The link deformation and the rotary joint motion are described as link and joint homogeneous transformation matrices. The link transformation matrix between the two coordinate systems assigned at both ends is obtained by using the assumed-mode method. The Lagrange-Euler equation is then used to formulate the dynamic equations of motion. The equations of motion of the flexible manipulator in the vector-matrix form as shown in equation (12) are coupled, nonlinear, second-order differential equations. With these equations it is possible to design control laws to compensate for the nonlinear effects. Preliminary simulation results from both rigid and flexible models indicate the feasibility of the model.