• DECEMBER 2019
     Rigid Body Dynamics
     Time Integration Method – Lesson 4
         Rigid Body Dynamics
        We discussed solving dynamics problem by implicit and explicit methods to obtain the response of 
        structures under dynamic loads. The outputs included deformation, stress, strain, etc. For large-scale 
        and long-duration dynamics problems, the computation cost to solve them are significant. In some 
        cases, when deformation of material is not the main concern, but the rigid motion is the response 
        engineers are looking for, rigid dynamics is the right path. This applies when:
        •  Objects are very stiff.
        •  Deformation of material points is not important.
        •  You are dealing with a large-scale, complex system.
           No need to solve for things you don’t care about. Assume perfect rigid bodies!
        •  The structural stiffness K is removed from the equation of motion.
        •  Different rigid parts are linked by joints/contacts.
   Rigid Body Dynamics (cont.)
            Hardball         Rigid Motion
            Softball         Distortion
         Rigid Body Dynamics: Degrees of Freedom (DOFs)
        Unlike dynamics for flexible bodies which looks for deformation at each material point, rigid body 
        dynamics looks for the rigid motion of the system. Especially, it solves for relative displacement 
        between different parts.
                                                                                                                     Revolute joint
                                                                     5x2 = 10 
                                                               constraint equation
                          Revolute joint
                                 6x2 = 12 DOF                                                                        5 Constrained: 
                                                                                                                 Ux, Uy, Uz, ROTx, ROTy
        •   One rigid body has at most 6 degrees of freedom in 3D space.                                              1 Free: ROTz
        •   The number of DOFs is largely reduced if using relative DOFs.
        •   Because parts are rigid, relative DOFs are sufficient to describe the mechanism.