VM-EXD-MECH-008

VM-EXD-MECH-008
Projector Mechanism -- Finding the Acceleration of a Point

Overview

Reference:	Any Basic Kinematics Book
Analysis Type(s):	Explicit Dynamics 3-D (Fully Rigid)
Elements:	Rigid Body Elements
Boundary Conditions:	Fixed Constraint, Joint Load (Rotational Velocity)
Structural Interactions:	No
Fluid-Structure Interactions:	No
Connections:	Revolute Joint
Materials:	Steel

The mechanism shown is used to pull a movie through a projector:

Figure 245: Mechanism Schematic

The mechanism is driven by the drive wheel rotating at a constant -58.643 rad/s. All link lengths are constant:

The horizontal distance between A and C is length = 34 mm.

The analysis determines the acceleration of point C with a change of angle of link AB (θ ₁) from 0 to 60 degrees in a counter-clockwise direction.

Material Properties

Geometric Properties

E = 2e11 Pa

ν = 0.3

r₁ = 18 mm

r₂ = 48 mm

x = 45 mm

y = 28 mm

Constant rotational velocity = -58.643 rad/s

Linear acceleration of point C (in Figure 245: Mechanism Schematic) is given by:

Results	Target	Explicit Dynamics [1]	Error (%)
Relative acceleration (θ ₁ = 10) mm/s²	-12.06	-12.128	0.564
Relative acceleration (θ ₁ = 30) mm/s²	1.317	1.3155	-0.114
Relative acceleration (θ ₁ = 60) mm/s²	6.739	6.7601	0.313

To compare these results to those obtained using rigid body dynamics, see VM-WB-MECH-055.