Joint Constraints and Kinematics

Constraint Stabilization for DAE Systems was Invented by Baumgarte (1972)

Constraints in multibody systems give rise to Differential Algebraic Equations (DAE). The numerical stability problem of these DAEs was solved by J. Baumgarte's 1972 proposal of the "Constraint Stabilization Method (Baumgarte Stabilization)". It was a simple idea of adding feedback gains to the constraint condition Φ and its velocity level Φ˙ to dampen errors, but "appropriate gain selection" proved difficult and became a topic of debate for many years. The Gear-Gupta-Leimkuhler (GGL) method (1985) solved this problem algebraically and significantly improved the integration accuracy of MBD solvers.

For 6-DOF Description of Rigid Body MBD, Quaternions are Better than Euler Angles

Euler angles, which represent rigid body orientation, have a singularity problem called "gimbal lock". Since the NASA Apollo 13 (1970) incident where gimbal lock became a problem in spacecraft attitude control, rotation representation using quaternions (four-element numbers) has become standard in MBD solvers. Quaternions use 4 parameters to represent 3 degrees of freedom, making them redundant, but they have no singularities and are numerically stable for computer operations. MSC Adams transitioned to internal quaternion representation in the late 1980s, drastically reducing crash reports due to singularities.

Virtual Joints for Suspensions Originated from CATIA DMU

When modeling automotive multi-link suspensions in MBD, the technique of replacing physical bushings (rubber elastic bodies) with "equivalent rigid joints" was popularized by CATIA Digital Mockup (DMU Kinematics) in the 1990s. Approximating the nonlinear characteristics of bushings with equivalent linear joints can speed up calculations by tens of times. Toyota's production engineering department published an SAE paper disclosing that they incorporated this technique into the mass production design process for stroke analysis of the Hilux (Land Cruiser series) suspension.

Simpack Has Adoption Record for Shinkansen (Bullet Train) Bogie MBD

Simpack by German Simula (now Dassault Systèmes) holds market share in the industry with features specialized for railway vehicle dynamics analysis. It was adopted by JR Central for joint and wheel flange contact analysis of the Tokaido Shinkansen N700 series bogies, and contributed to the design for suppressing hunting oscillation at speeds over 350 km/h, as confirmed in publications by the Railway Technical Research Institute. SIMPACK 2022 added VR integration features enabling real-time co-simulation to check NL behavior of contact joints.

Redundant Constraints are Rank