MBS Benchmark A02: N-Four-Bar Mechanism

Benchmark Objective

The A02 MBS benchmark problem is a common example of a mechanism which undergoes singular configuration.

Benchmark Description

The N-four-bar mechanism is a common example of a mechanism which undergoes singular configuration. The system has N four-bar windows composed of 2N+1 links. It is an extension of the two four-bar mechanism proposed in [BA94]. When the mechanism reaches the horizontal position, the number of the degrees of freedom instantaneously increase from 1 to N+1. Gravity acts on the negative y direction.

N-four-bar mechanism sketch.

The following table reports the initial configuration of the system.

System Properties and Configuration
N 2
Link mass 1.0 Kg
Link length 1.0 m
\(\dot{B_{0}x}(0)\) 1.0 m/s


The dynamic simulation of the A02 benchmark was executed for a period of 10 seconds. The starting position of the simulation is shown in the previous picture with an initial speed for the point \(B_0\) in the positive x-direction of 1 m/s.

The accuracy of the simulation has been measured as the variation in the mechanical energy from the initial condition. Mechanical energy defined as the sum of potential and kinetic energy. Since no dissipation phenomena is included in problem definition, theoretical value for mechanical energy variation shoud be zero.

Additional evaluation has been conducted comparing the simulated displacement of the point \(B_0\), with the reference solution provided by the problem authors [GDLC06].

The simulation with OpenSim perfectly matches the reference values.

A02 energy.

Figure 5: Mechanical energy variation during simulation period from the initial condition. Theoretical variation (black line) and simulated one (blue line).

A02 kinematics.

Figure 6: Displacement of reference point \(B_0\) in OpenSim simulation (colored lines) and MBS benchmark reference (black dashed lines).

Computational Performances

To compute the simulation the developed implementation required 0.455 seconds.

Results obtained using an Intel Core i5-4570 @ 3.2 GHz computer running Windows 8.1 64-bit. OpenSim official release used: 3.2.

Comparision with other dynamic engines has been conducted submitting the obtained results to the benchmark collaborative library. Click here to see the comparison results.