Managing Redundant Constraints and Joint Primitives in Multibody Dynamics

Welcome to the Multibody Dynamics for Automotive Applications using MotionView and MotionSolve blog series! In this chapter, we explore redundant constraints, joint primitives, and motion functions. These concepts are crucial for multibody dynamics simulation, vehicle dynamics simulation, and automotive engineering simulation.

Understanding Redundant Constraints

When building a multibody dynamics model, it is possible to over-specify constraints, leading to a condition known as an over-constrained system. This occurs when multiple constraints restrict the same degrees of freedom, making some constraints redundant.

For example, consider a door attached to a frame with three hinges. A rigid body has six degrees of freedom (DOF), and each revolute joint removes five DOF, allowing only one rotational DOF. If we add three hinges, the total DOF calculation would be: Since the DOF becomes negative, the system has redundant constraints, making some joints unnecessary for simulation accuracy. MotionSolve automatically detects and removes redundant constraints, but this can affect reaction force calculations.

Methods to Remove Redundant Constraints

To avoid redundant constraints in multibody dynamics analysis, consider:

• Using Joint Primitives (JPRs) – These provide specific constraint definitions without over-constraining the system.
• Applying Compliant Joints or Bushings – These allow flexibility and help reduce redundancy.
• Using Flexible Bodies – Instead of rigid bodies, flexible bodies provide more realistic behavior but increase computational cost.

Types of Constraints in MotionView

In multibody dynamics using MotionView, constraints are categorized into:

• Lower Pair Constraints – Idealized joints with real-world mechanical analogies (e.g., revolute, cylindrical joints).
• Joint Primitives (JPRs) – Used for fine-tuned constraint control.
• Higher Pair Constraints – Used for contacts between surfaces (e.g., cams, bearings).
• Motions – Define prescribed displacements, velocities, or accelerations.
• Other Constraints – Custom algebraic relations (e.g., gear couplers).

Joint Primitives (JPRs) in MotionView

JPRs help define specific translational and rotational constraints. Common JPRs include:

• At Point – Removes three translational DOFs.
• Inline Joint – Removes two translational DOFs.
• In-Plane Joint – Removes one translational DOF.
• Orientation Constraint – Removes three rotational DOFs.
• Parallel Axis Constraint – Removes two rotational DOFs.
• Perpendicular Axis Constraint – Removes one rotational DOF.

Application of Joint Primitives: The In-Plane JPR

The In-Plane Joint Primitive is a widely used JPR. It ensures that the origin of a reference marker on Body 1 remains within the XY plane of a reference marker on Body 2. This effectively removes one translational DOF along the Z-axis.

One common application of this JPR is in suspension test rigs, such as the two-post or four-post rig for automotive suspension system analysis.

Understanding Motion Functions in MotionSolve

Motion functions in MotionSolve software help compute forces and torques in constrained motion systems. The syntax for defining motion functions is: Where:

• ID: Identifies the motion entity.
• J-Flag: Determines force/torque calculation at I-Marker (0) or J-Marker (1).
• Component: Specifies whether to extract force magnitude, torque, or directional components.
• Reference Marker (RM): Defines the coordinate frame (0 = Global Reference Frame).

For example:

• Component = 1 – Extracts force magnitude.
• Component = 5 – Extracts torque magnitude.
• Component = 6, 7, 8 – Extracts X, Y, and Z components of torque, respectively.

Conclusion

Understanding redundant constraints, joint primitives, and motion functions is essential in multibody dynamics training and certification. These concepts help improve model accuracy while preventing over-constraining the system in vehicle dynamics software.

Stay tuned for the next blog, where we explore advanced constraint management techniques and practical applications in MotionView and MotionSolve!

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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