Mechanism Simulation: Checking Motion Before Metal Is Cut

A linkage looks smooth in the sketch and binds in the prototype. The four-bar that seemed to swing through the range hits the limit at the wrong point. The cam that was drawn from the handbook profile jerks at the high speed. Mechanism simulation is the tool that catches these problems while the design is still a mouse click away from a change. This article covers what mechanism simulation does, what it cannot do, and how to use it without overbuilding the model.

What Mechanism Simulation Answers

Mechanism simulation answers three questions that a static model cannot. The first is the motion range: does the linkage travel through the required positions without reaching a singularity or a lock? The second is the velocity and the acceleration: does the mechanism jerk at the speed it will actually run? The third is the force: does the actuator have the torque to move the load through the whole cycle?

The answers come from the kinematic and the dynamic analysis. The kinematic analysis tracks the positions, the velocities, and the accelerations of the links, ignoring the forces. The dynamic analysis adds the masses, the inertias, and the forces, and computes the required actuator torque and the joint reactions.

The value is the early discovery. The linkage that binds at the extreme position is discovered in the simulation session, not in the assembly bay. The actuator that is undersized is discovered when the motor is still a catalog number, not when the machine is on the floor.

The Model That Is Good Enough

The simulation model does not need the full CAD detail. The linkage is modeled as the links with the joint positions. The cam is modeled as the profile and the follower. The mass properties are entered from the real parts, but the cosmetic geometry is left out.

The rule: the simulation model needs the joint locations, the link lengths, and the masses. The joint locations and the link lengths drive the kinematics. The masses and the inertias drive the dynamics. The fillets, the holes, and the bosses do not matter to the simulation, and they slow the solver.

The model should be checked against the real geometry. The joint locations in the simulation must match the joint locations in the CAD assembly. The mismatch of a few millimeters changes the acceleration curve, and the changed curve changes the force calculation.

The Motion Study Workflow

The motion study starts with the assembly in the CAD software. The mates define the joints: the revolute joints for the pivots, the prismatic joints for the slides, the cylindrical joints for the shafts.

The next step is the motion input. The actuator is defined by its motion: the cylinder stroke as a function of time, the motor speed as a function of time, the cam rotation at the constant speed. The input profile should include the acceleration and the deceleration, because the real actuator does not start and stop instantly.

The solver runs the analysis and outputs the plots. The position plot shows the travel. The velocity plot shows the speed profile. The acceleration plot shows the jerk. The force plot shows the actuator load and the joint reactions.

The plots are read with the eye on the extremes. The acceleration spike at the end of the stroke, the force peak at the start of the cycle, and the velocity dip at the changeover are the signals that the mechanism needs attention.

The Common Mechanism Failures

The first failure is the toggle position. The linkage that reaches the straight line between the pivots has no mechanical advantage at that position, and the actuator force goes to infinity as the mechanism approaches the toggle. The simulation shows the force spike, and the design moves the pivots or adds the stop before the toggle.

The second failure is the transmission angle. The angle between the coupler and the follower at the joint should stay above about thirty degrees. The low transmission angle makes the mechanism sluggish and the joint forces high. The simulation shows the angle, and the design changes the link lengths to keep the angle healthy.

The third failure is the interference at the extreme. The links that swing through the range and collide with the frame or the other links at the extreme position. The simulation with the clearance envelopes shows the collision while the design is still changeable.

The fourth failure is the inertia mismatch. The mechanism that accelerates a heavy load with a small actuator stalls or jerks. The simulation with the real masses shows the required torque, and the actuator is sized from the number.

The Actuator Sizing

The actuator sizing is the most practical output of the simulation. The cylinder, the motor, and the linear actuator are sized from the peak torque or the peak force, not from the average.

The peak torque comes from the dynamic analysis with the worst-case load. The worst case includes the load, the inertia, and the friction. The friction is estimated from the coefficient and the normal forces, and the estimate is conservative.

The actuator is then selected with the margin. The peak torque from the simulation is multiplied by the service factor, typically 1.2 to 1.5 for the industrial mechanisms. The margin covers the friction variation, the temperature effect, and the wear.

The acceleration time is checked too. The actuator that has the peak torque but cannot accelerate the load to the required speed in the required time is the actuator that fails the cycle time. The simulation gives the acceleration curve, and the curve is checked against the cycle time budget.

The Validation Loop

The simulation is a model, and the model needs the validation. The first prototype run is the validation of the simulation. The measured cycle time, the measured force, and the measured behavior are compared to the simulation.

The comparison is the calibration. The friction that was estimated is refined from the measurement. The inertia that was entered is corrected. The refined model is the model that predicts the next mechanism.

The simulation that is never validated is the simulation that will be trusted once too often. The team that validates the first mechanism of each type builds the confidence that makes the simulation useful for the next.

Conclusion

Mechanism simulation checks the motion before the metal is cut. Model the links and the joints, run the motion study with the real input, read the plots for the toggles and the transmission angles and the interferences, size the actuator from the peak values with the margin, and validate the first prototype against the model. The mechanism that is simulated well is the mechanism that works the first time, and the first-time mechanisms are the schedule savers.

The Simulation Software Landscape

The mechanism simulation is available at every level, and the choice depends on the need. The CAD package includes the motion study module that handles the common mechanisms. The dedicated multibody software handles the complex machines with the flexible bodies and the detailed contacts. The open-source packages handle the academic and the simple industrial cases.

The CAD motion study is the fastest start. The assembly mates become the joints, the motion inputs are applied, and the plots come out. The CAD motion study handles the linkages, the cams, and the simple dynamics with the point masses. The limitation is the detail: the friction, the contact, and the flexible bodies are simplified.

The dedicated multibody software adds the detail. The flexible bodies, the bushing elements, the detailed friction models, and the control system integration are available. The price is the model complexity and the solver time. The complex machine with the closed loops and the elastic members is the case that justifies the dedicated tool.

The simulation is also available in the programming environment. The Python libraries and the MATLAB tools model the mechanism with the equations of motion. The programmable approach gives the full control and the insight into the math, at the cost of the modeling effort.

The rule: use the simplest tool that answers the question. The four-bar linkage is checked in the CAD motion study. The packaging machine with the cams, the springs, and the servo loops goes to the multibody software. The research question goes to the code.

The Model Preparation

The mechanism simulation is only as good as the model preparation, and the preparation follows a repeatable sequence. The first step is the identification of the joints and the links from the CAD assembly. The parts that move relative to each other are the links, and the connections between them are the joints.

The second step is the simplification. The bolted assembly that moves as one body is merged into a single link. The bearing that allows the rotation is replaced by the revolute joint. The cosmetic features are suppressed. The model that is simplified to the joints and the links solves fast and reads clear.

The third step is the verification of the degrees of freedom. The mechanism should have the expected number of the degrees of freedom. The over-constrained model locks the solver, and the under-constrained model floats. The mobility check is done with the Gruebler equation or with the solver’s own diagnostic.

The fourth step is the input definition. The motion input is the profile of the actuator: the displacement or the velocity as a function of time. The profile is entered with the acceleration and the deceleration, and the initial conditions are set.

The fifth step is the output selection. The positions, the velocities, the accelerations, and the forces are the standard outputs. The plots and the tabulated data are selected before the run, and the run produces the results in the format that the review needs.

A Worked Example: The Pick-and-Place Linkage

A pick-and-place mechanism shows the workflow. The machine places the small parts from the conveyor to the nest at the cycle time of one second. The design uses a four-bar linkage driven by the servo motor.

The motion study starts with the joint locations from the CAD assembly. The crank length, the coupler length, the rocker length, and the ground pivot positions are entered. The servo motor input is defined with the trapezoidal velocity profile: the acceleration, the constant speed, and the deceleration.

The first simulation run shows the motion range. The linkage swings through the pickup position and the place position, and the plots show the travel. The simulation also shows the transmission angle, and the angle dips below the healthy thirty degrees at one extreme.

The design change moves the ground pivot to improve the transmission angle. The second run shows the healthier angle. The velocity and the acceleration plots show the peak values, and the peak acceleration at the endpoints is the value that drives the inertial load.

The dynamic analysis adds the masses. The coupler mass, the end effector mass, and the part mass are entered. The required motor torque is plotted, and the peak torque occurs at the acceleration phase. The peak torque is multiplied by the service factor, and the motor is selected from the catalog.

The prototype validates the simulation. The cycle time matches, the motion looks smooth, and the motor runs at the predicted load. The simulation is calibrated, and the next similar mechanism is designed with the confidence.

The Limits of the Simulation

The simulation is a model, and the model has the limits. The joint clearance that is neglected, the friction that is estimated, and the flexibility that is ignored are the differences between the model and the machine.

The joint clearance causes the impact and the noise. The revolute joint with the clearance has the free play that the model does not show. The mechanism that runs quiet in the simulation and noisy on the floor is often the mechanism with the clearance that the model ignored.

The friction is the second difference. The static and the dynamic friction in the joints, the seals, and the guides are estimated with the coefficients. The estimate is the source of the uncertainty in the force results.

The flexibility is the third. The links that bend, the shafts that twist, and the frame that flexes change the dynamic behavior. The mechanism that is modeled as the rigid bodies is the mechanism that is stiffer than the real machine.

The simulation limits are handled with the margins. The force results are used with the service factor, the clearance is designed out with the tight fits, and the validation prototype checks the predictions. The simulation that is used with the respect for the limits is the simulation that earns the trust.