Understanding Redundant Constraints in Multibody Dynamics Simulation

Welcome to the Multibody Dynamics for Automotive Applications using MotionView and MotionSolve blog series! 

In this chapter, we delve into the concept of redundant constraints, a crucial aspect of multibody dynamics simulation. When building a model in MotionView, it is common to over-specify constraints, leading to an over-constrained system. Understanding how to detect and remove redundant constraints ensures accurate and efficient simulations in multibody dynamics for automotive applications. 

What are Redundant Constraints? 

A system is said to be over-constrained when unnecessary constraints are added, restricting degrees of freedom beyond what is required. To illustrate, consider the mathematical equation: 

Adding another identical equation results in: 

• This additional equation does not introduce new information, making it redundant. Similarly, in multibody dynamics modeling, redundant constraints do not contribute to system stability and must be eliminated. 
• Example: Door Hinges and Redundant Constraints 

Consider a rigid door attached to a frame using three hinges. Each hinge represents a revolute joint, which removes five degrees of freedom (three translational and two rotational). Since the door itself has six degrees of freedom, three revolute joints completely over-constrain the system:

• A negative degree of freedom indicates redundant constraints, meaning two hinges are unnecessary for accurate motion simulation. In MotionSolve, the solver detects and removes redundant constraints automatically, which may alter expected reaction forces and torque values. 

Methods to Remove Redundant Constraints 

Redundant constraints can be eliminated using: 

• Lower Pair Joints (Joint Primitives): Used to model complex mechanisms without redundancy. 
• Compliant Joints (Bushings): Introduces flexibility to handle minor misalignments. 
• Flexible Bodies: Instead of rigid bodies, flexible components allow for realistic motion, reducing constraint redundancy. 

Classifying Constraints in MotionView 

Constraints in MotionView software are categorized into: 

• Lower Pair Constraints: Ideal joints restricting point/line/plane contact. 
• Joint Primitives (JPRs): Used in combination with other joints. 
• Higher Pair Constraints: Involves point or line contact (e.g., cam-follower systems). 
• Motion Constraints: Prescribes displacement, velocity, or acceleration. 
• Other Constraints: Used for algebraic relationships (e.g., couplers, gears). 

By implementing best practices in multibody dynamics modeling, redundant constraints can be effectively managed, ensuring accurate vehicle dynamics simulation and optimized computational performance. Stay tuned for our next blog, where we apply these concepts in a four-bar mechanism simulation using MotionView for automotive engineers! 

This blog is part of our ongoing Multibody Dynamics blog series. If you missed the previous posts, check them out here.  

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