1 IntroductionThe subject of this a

1 Introduction
The subject of this article is the VEProject Shifted Lever video, as found at the following
URL:
https://www.youtube.com/watch?v=8TniRMwL2Vg&list=PLpvrrzoPjcITuqx5t6nYpAnM4nyWp
The video shows a "Shifted Lever" mechanism, a device that appears to be perpetually o¤
balance. It is presented as a perpetual motion mechanism, that is, a machine that will run
forever without any energy input other than, perhaps, an initial push. This presentation
comes from the VEProject, where VEProject stands for "Visual Education Project." An
educational project can be presumed to be a presentation of truth, so should we accept
that the author believes that this device is truly a perpetual motion device, or that he is
attempting to deceive the viewer?
As most Mechanical Engineers know, the laws of thermodynamics show that there cannot be
perpetual motion. So, are the laws of thermodynamics incorrect, or are we being deceived?
Fig. 1 Shifted Lever Mechanism
Let us investigate. The video shows a pair of three-armed stars, each supporting a weighted
lever to the left, as shown in Fig. 1. The two stars are one behind the other, with their
centers vertically displaced a distance h, as shown in Fig. 2. At the tip of each lever, there is
a link (of vertical length h) that joins the two stars, keeping their rotations in synchronism.
This link also has a horizontal dimension equal to the horizontal separation between the two
stars. A "‡ag" is attached rigidly to the horizontal leg of the coupling link, so that as the
entire assembly rotates, the ‡ags all remain horizontal at all times. Fig. 1 shows a typical
1
position, displaced from having any leg straight up. In Fig. 2, one third of the complete
assembly is shown, consisting of adjacent arms of each star and the link and ‡ag connection
between the two of them.
2 Analysis
The analysis is built on the single arm assembly shown in Fig. 2. This is exactly 1/3 of
the complete device, so the extension of the analysis for the other two arms will be a simple
matter. The focus of the analysis is on the path of the system center of mass, because the
mechanism appears to be gravity driven.
Let the subscript 1 be associated with the front arm (lower and closest to the reader) while
subscript 2 is associated with the rear arm. The reference level for the calculation of gravi-
tational potential energy is the ground plane shown in Fig. 2 at the level of the pivot point
for the front star. The center of mass for an arm is a distance cL away from the pivot point
for the star, where 0 < c < L: The center of mass locations for the two arms involved are
xc1 = cL sin 
yc1 = cL cos 
xc2 = cL sin 
yc2 = h + cL cos 
where the vertical o¤set, h, is re‡ected in the expression for yc2.
L
h
h
b
a
a
q
g
x
y
Fig. 2 Single Arm Assembly
For simplicity, the center of mass of the vertical part of the coupling link is assumed to be
at the center of the vertical part, h=2 from either end. The center of mass location for this
leg is then
xcv = L sin 
ycv =
1
2
h + L cos 
2
The center of mass of the horizontal portion of the coupling link is at the lower pivot, so
that
xch = L sin 
ych = L cos 
The center of mass of the horizontal ‡ag pole is located at the center of its length, so that
xcp = L sin  +
1
2
b
ycp = L cos 
The ‡ag itself appears to be square, so its center of mass is at the geometric center,
xcf = L sin  +

b