A formulation of kinematic constraints imposed by kinematic pairs using relative pose in vector form
Tóm tắt
This paper presents a formulation that expresses kinematic pairs in form of holonomic constraints as functions of a measure of the relative position and orientation of the connected bodies expressed in vector form. While formulating the relative position measure is straightforward, expressing a suitable measure of the relative orientation requires some care. The problem is addressed by computing the Euler vector of the product of the actual and prescribed relative rotation matrices. By arbitrarily combining the error measures in up to six independent equations, a general family of holonomic rheonomic constraints can be formulated. The relative motion between the bodies can be constrained or specified component-wise, respectively, resulting in scleronomic or rheonomic constraints. The proposed formulation is implemented in a free, general-purpose multibody solver; numerical applications to generic mechanical and aerospace problems are presented.
Tài liệu tham khảo
Schiehlen, W.: Multibody system dynamics: roots and perspectives. Multibody Syst. Dyn. 1(2), 149–188 (1997). doi:10.1023/A:1009745432698
Bauchau, O.A., Laulusa, A.: Review of contemporary approaches for constraint enforcement in multibody systems. J. Comput. Nonlinear Dyn. 3(1) (2008). doi:10.1115/1.2803258
Masarati, P., Morandini, M.: An ideal homokinetic joint formulation for general-purpose multibody real-time simulation. Multibody Syst. Dyn. 20(3), 251–270 (2008). doi:10.1007/s11044-008-9112-8
Hartenberg, R.S., Denavit, J.: Kinematic Synthesis of Linkages. McGraw-Hill, New York (1964)
Angeles, J.: Spatial Kinematic Chains. Springer, Berlin (1982)
Angeles, J.: Fundamentals of Robotic Mechanical Systems—Theory, Methods, and Algorithms, 3rd edn. Springer, Berlin (2007)
Bauchau, O.A.: Flexible Multibody Dynamics. Springer, Dordrecht (2010)
García de Jalón, J., Serna, M.A., Avilés, R.: Computer method for kinematic analysis of lower-pair mechanisms—I velocities and accelerations. Mech. Mach. Theory 16(5), 543–556 (1981). doi:10.1016/0094-114X(81)90026-4
García de Jalón, J., Bayo, E.: Kinematic and Dynamic Simulation of Multibody Systems: The Real Time Challenge. Springer, New York (1994)
García-Vallejo, D., Mayo, J., Escalona, J.L., Domínguez, J.: Modelling three-dimensional rigid-flexible multibody systems by using absolute coordinates. In: 12th IFToMM World Congress, Besançon, France, June 18–21, pp. 1–6 (2007)
García-Vallejo, D., Mayo, J., Escalona, J.L., Domínguez, J.: Describing rigid-flexible multibody systems using absolute coordinates. Nonlinear Dyn. 34(1–2), 75–94 (2003). doi:10.1023/B:NODY.0000014553.98731.8d
Sugiyama, H., Escalona, J.L., Shabana, A.A.: Formulation of three-dimensional joint constraints using the absolute nodal coordinates. Nonlinear Dyn. 31(2), 167–195 (2003). doi:10.1023/A:1022082826627
Hussein, B.A., Weed, D., Shabana, A.A.: Clamped end conditions and cross section deformation in the finite element absolute nodal coordinate formulation. Multibody Syst. Dyn. 21(4), 375–393 (2009). doi:10.1007/s11044-009-9146-6
Sugiyama, H., Yamashita, H.: Spatial joint constraints for the absolute nodal coordinate formulation using the non-generalized intermediate coordinates. Multibody Syst. Dyn. 26(1), 15–36 (2011). doi:10.1007/s11044-010-9236-5
Bauchau, O.A., Trainelli, L.: The vectorial parameterization of rotation. Nonlinear Dyn. 32(1), 71–92 (2003). doi:10.1023/A:1024265401576
Pfister, F.: Bernoulli numbers and rotational kinematics. J. Appl. Mech. 65(3), 758–763 (1998). doi:10.1115/1.2789120
Betsch, P., Menzel, A., Stein, E.: On the parametrization of finite rotations in computational mechanics. A classification of concepts with application to smooth shells. Comput. Methods Appl. Mech. Eng. 155(3–4), 273–305 (1998). doi:10.1016/S0045-7825(97)00158-8
Borri, M., Trainelli, L., Bottasso, C.L.: On representations and parametrizations of motion. Multibody Syst. Dyn. 4(2–3), 129–193 (2000). doi:10.1023/A:1009830626597