Understanding Constraints in Multibody Dynamics: Degrees of Freedom and Joint Types

Welcome to the Multibody Dynamics for Automotive Applications using MotionView and MotionSolve blog series! In this chapter, we will explore the concept of constraints in multibody dynamics simulation. Constraints, such as joints and motions, are essential in controlling the behavior of interacting bodies in multibody dynamics using MotionView. Understanding degrees of freedom (DOF) and how constraints affect motion is crucial for vehicle system modeling and automotive engineering simulation. 

Step 1: Understanding Degrees of Freedom (DOF) 

The degree of freedom of a system refers to the number of independent relative motions that define its configuration. Every rigid body has six degrees of freedom (three translations and three rotations): 

• Translation along the X, Y, and Z axes. 
• Rotation about the X, Y, and Z axes. 

The DOF of a system is calculated using Gersh’s Equation

Step 2: Visualizing Degrees of Freedom with Examples 

Consider a rigid box in free space: 

• It has 6 degrees of freedom. 
• Adding a fixed surface constraint restricts 1 DOF, reducing the system to 5 DOF. 
• Replacing a sphere with a cylinder further reduces DOF to 4. 
• Changing a cylinder to a cube restricts additional motion, leaving 3 DOF. 
• Introducing a shaft within a coaxial cylinder results in only 2 DOF. 
• Constraining translation results in a 1 DOF system. 

Step 3: Difference Between Kinematic and Dynamic Simulations 

• Dynamic Simulation: Calculates acceleration and forces when an initial velocity is provided. 
• Kinematic Simulation: Motion is predefined, removing all degrees of freedom. 

For example, applying translation motion to a sled with 1 DOF removes that freedom, making the analysis kinematic instead of dynamic. 

Step 4: Types of Joints in MotionView 

Joints restrict motion by removing specific degrees of freedom: 

• Revolute Joint: Removes three translational and two rotational DOF. 
• Spherical Joint: Removes three translational DOF, allowing full rotation. 
• Fixed Joint: Removes all six DOF. 
• Cylindrical Joint: Removes two translational and two rotational DOF. 

Step 5: Significance of Markers in Joints 

Markers play a critical role in defining joints in MotionView: 

1. I-Marker: Defined on the first body. 
2. J-Marker: Defined on the second body. 
3. Used to dictate relative motion between two bodies. 

Stay tuned for the next blog, where we will explore compliant joints and practical implementation of constraints in MotionView. 

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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