SimMechanics

Simulating Mechanical Motion

SimMechanics Analysis Modes

SimMechanics provides four modes for analyzing the mechanical systems you simulate:

• Forward dynamic analysis integrates applied forces/torques, maintaining imposed constraints, and obtains resulting motions.
• Inverse dynamic analysis finds the forces/torques necessary to produce user-specified motions in topologically open systems.
• Kinematic analysis finds the forces/torques necessary to produce user-specified motions in topologically closed (loop) systems.
• Trimming analysis searches for steady or equilibrium states of a system.

In the Conveyor Loader demo model, you analyzed the motion in the Forward Dynamics mode. The model specified forces/torques and initial conditions, then integrated Newton's laws to obtain the machine's motion.

Mathematical Conditions for Rigid Body Motion to Be Determined.   For the Forward Dynamics problem to be mathematically solvable, the system must satisfy certain conditions:

• The masses and inertia tensors of all bodies are known.
• All forces and torques acting on each body at each instant of time are known.
• Any constraints among DoFs are specified as constraints among positions and/or velocities alone. These are kinematic constraints; that is, zeroth- and first-order differential constraints. If the constraints are mutually consistent and are fewer in number than the DoFs, the system's motion is nontrivial and can be found by integration.
• Initial conditions (initial positions and velocities) are specified and consistent with all constraints.

In Inverse Dynamics or Kinematics analysis modes, you specify the motions instead and obtain the forces/torques needed to produce those motions.

Forward Dynamics

In the Forward Dynamics mode, SimMechanics uses the Simulink suite of ordinary differential equation (ODE) solvers to solve the mechanical ODEs (Newton's equations). The ODE solvers project the motion of the DoFs onto the mathematical manifold of the kinematic constraints and yield the forces/torques of constraint acting within the system.

You can also use the Simulink linearization tool to linearize the forward motion of a system and obtain its response to small perturbations in forces/torques, constraints, and/or initial conditions.

Inverse Dynamics

SimMechanics can solve the reverse of the forward dynamics problem: instead of starting with given forces/torques and finding the resulting motions, the Inverse Dynamics mode determines the forces/torques needed to produce a given set of motions that you apply to the machine. This mode only works with open topology systems (model diagrams without closed loops).

Kinematics

You cannot analyze machines represented by model diagrams with closed topology (models with loops) using the Inverse Dynamics mode. The Kinematics mode analyzes the motion of closed-loop models, including the extra internal invisible constraints arising from loop closures.

You also use the Kinematics mode to determine the forces/torques needed to produce a given set of motions applied to a closed-loop machine model.

Constraints can only appear in closed loops, so you use the Kinematics mode to analyze constraint forces/torques as well.

Trimming

Finally, the Trimming mode searches for steady or equilibrium states in a system's motion using the Simulink trim command. The states, once found, are the starting point for linearization analysis using the Simulink linmod and dlinmod commands.

Bodies, Coordinate Systems, Joints, and Constraints

Visualizing and Animating Machines