VM-EXD-MECH-011

VM-EXD-MECH-011
Reverse Four Bar Linkage Mechanism

Overview

Reference:	Results are simulated using MATLAB
Analysis Type(s):	Explicit Dynamics 3-D (Fully Rigid)
Elements:	Rigid Body Elements
Boundary Conditions:	Fixed Constraint, Gravity
Structural Interactions:	No
Fluid-Structure Interactions:	No
Connections:	Revolute
Materials:	Steel

Test Case

Shown is a reverse four bar linkage mechanism consisting of uniform rigid links PQ, QR, and RS and ground PS:

Figure 248: Reverse Four Bar Linkage Schematic

Link PQ is connected via revolute joints to links QR and PS at points Q and P, respectively. Link RS is connected via revolute joints to links QR and PS at points R and S, respectively.

The lengths of all links are constant:

Fixed Link PS length r₁ = 0.5 m
Crank Link PQ length r₂ = 0.15 m
Link QR length r₃ = 0.4 m
Link RS length r₄ = 0.45 m

Gravity g = 9.81 m/sec²

Determine the angular accelerations, angular velocity and rotation of link RS at joint R.

Material Properties	Geometric Properties	Loading
E = 2 x 10¹¹ Pa ν = 0.3	Link PS length r₁ = 0.5 m Link PQ length r₂ = 0.15 m Link QR length r₃ = 0.4 m Link RS length r₄ = 0.45 m	Gravitational acceleration = -9.8066 m/s² (Y direction)

Material Properties

Geometric Properties

E = 2 x 10¹¹ Pa

ν = 0.3

Link PS length r₁ = 0.5 m

Link PQ length r₂ = 0.15 m

Link QR length r₃ = 0.4 m

Link RS length r₄ = 0.45 m

Gravitational acceleration = -9.8066 m/s² (Y direction)

Analysis

Results are obtained using MATLAB.

Results Comparison

Results	Target	Explicit Dynamics [1]	Error (%)
Angular Acceleration (rad/s²)	39.268	39.266	0.0051
Angular Velocity (rad/sec)	-5.13	-5.1319	0.0370
Rotation (rad)	-0.36	-0.36091	0.253

To compare these results to those obtained using rigid body dynamics, see VM-WB-MECH-058.