VM-WB-MECH-055

VM-WB-MECH-055
Projector Mechanism - Finding the Acceleration of a Point

Overview

Reference:	Any Basic Kinematics Book
Solver(s):	Ansys Mechanical
Analysis Type(s):	Rigid Dynamic Analysis
Element Type(s):	Multipoint Constraint Element

Test Case

The mechanism shown in figure is used to pull a movie through a projector. The mechanism is driven by the drive wheel rotating at a constant -58.643 rad/s. All link lengths are constant:

Link AB length r₁ = 18mm
Link BC length r₂ = 48mm
Length BX = x = 45 mm and CX = y = 28 mm

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.

Figure 73: Schematic

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

Analysis

Linear acceleration of point C is given by:

Results Comparison

Results	Target	Mechanical [1]	Error (%)
Relative acceleration (θ ₁ = 10) mm/s²	-12.06	-12.043	-0.141
Relative acceleration (θ ₁ = 30) mm/s²	1.317	1.3168	-0.015
Relative acceleration (θ ₁ = 60) mm/s²	6.739	6.7386	-0.006

To compare these results to those obtained using explicit dynamics, see VM-EXD-MECH-008.