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International Journal of Mechanical Engineering Education 32/2
Quick-return mechanism design and analysis
projects
Ron P. Podhorodeski, Scott B. Nokleby and Jonathan D. Wittchen
Robotics and Mechanisms Laboratory, Department of Mechanical Engineering, University of
Victoria, PO Box 3055, Victoria, British Columbia, Canada, V8W 3P6
E-mail: podhoro@me.uvic.ca; snokleby@me.uvic.ca; jwittchen@crsrobotics.com
Abstract Quick-return (QR) mechanisms feature different input durations for their working and return
strokes. The time ratio (TR) of a QR mechanism is the ratio of the change in input displacement during
the working stroke to its change during the return stroke. Several basic types of mechanism have a QR
action. These types include slider-crank and four-bar mechanisms. A project on QR mechanism design,
within a first course on the theory of mechanisms, has been found to be effective for exposing students
to concepts of mechanism design and analysis. This paper reviews basic QR mechanisms, presents a
project problem and solution examples, and discusses the value of inclusion of such project problems
within theory-of-mechanism courses.
Keywords mechanism projects; design; analysis; synthesis
Introduction
Quick-return mechanisms
Quick-return (QR) mechanisms feature different input durations for their working
and return strokes. The time ratio (TR) of a QR mechanism is the ratio of the change
in input displacement during the working stroke to its change during the return
stroke. QR mechanisms are used in shapers, power-driven saws, and many other
applications requiring a load-intensive working stroke in comparison to a low-load
return stroke [1–3].
Several basic types of mechanism have a QR action. These include slider-crank
mechanisms (e.g., see the offset slider-crank mechanism in Fig. 1a and the inverted
slider-crank mechanisms, including the crank-shaper mechanism, in Fig. 1b and the
Whitworth in Fig. 1c) and four-bar mechanisms (e.g., see the crank-rocker-driven
piston in Fig. 2a and the drag-link-driven piston in Fig. 2b).
Mechanism analysis techniques taught in a first course on the theory of mecha-
nisms can be applied to evaluate the performance of QR mechanisms. Design of a
mechanism, on the other hand, requires determining a mechanism to perform a
desired task. For example, synthesis of a reciprocating QR device requires determi-
nation of a mechanism to produce a desired TR and a necessary stroke. Note that
there is not necessarily a unique mechanism design for a particular task: many mech-
anism types (e.g., offset slider-crank, Whitworth, drag-link, etc.) may be capable of
performing it. Even within one mechanism type, many different link-length com-
binations (perhaps an infinity of several dimensions [1]) may perform the required
task.
Choosing a type of mechanism for a task is called type synthesis. Selecting link
lengths for a chosen type is referred to as dimensional synthesis [1–3]. When many
Quick-return mechanisms 101
International Journal of Mechanical Engineering Education 32/2
mechanisms of various types and/or dimensions that satisfy the primary task exist,
concerns such as mechanism size, minimum transmission angles, maximum accel-
erations, etc., can be considered to isolate a preferred design.
The task of a QR mechanism is simple to understand. Several concepts of design
and analysis can be illustrated by a QR mechanism project. For example, students
can be exposed to concepts of kinematic analysis, of minimum transmission angles,
of type and dimensional synthesis, and of computer-aided modelling programs.
Several techniques can be considered and developed by students to achieve the
required synthesis task; for example, physical modelling, graphical, iterative, and
analytical techniques can all be used to synthesize a desired mechanism. Having a
laboratory manual that briefly outlines different possible techniques, and leaves the
Fig. 1 Slider-crank QR mechanisms: (a) offset slider-crank, (b) crank-shaper, (c)
Whitworth.
102 R. P. Podhorodeski et al.
International Journal of Mechanical Engineering Education 32/2
student-applied technique open, requires a creative algorithm-design process. Over
the past 10 years at the Department of Mechanical Engineering, University of Vic-
toria, a variety of projects featuring different mechanism types have been used
within a first course on the theory of mechanisms. The QR project, along with similar
technique-open projects on inertia modelling and on cam design, has given the
students a strong appreciation of mechanism analysis and design issues, and has
allowed the assignment to the course of a significant percentage of accreditation
units (AUs) for Engineering design [4].1
The project described in this work is assigned to and completed by the students
within the first four weeks of a first course on mechanism analysis. This course
occurs in the first term of third year, of a semestered four-year academic programme
that leads to an accredited bachelor of engineering in mechanical engineering degree.
Fig. 2 Four-bar QR mechanisms: (a) crank-rocker as the driving mechanism, (b) drag-
link (crank-crank) as the driving mechanism.
1The Canadian Engineering Accreditation Board (CEAB) performs accreditation of all undergraduate
engineering programmes in Canada. AUs are assigned to the curriculum content of the courses within
the program under consideration. Currently AUs are divided between (a) mathematics, (b) basic sciences,
(c) engineering sciences, (d) engineering design, and (e) complementary studies. Quoting CEAB Accred-
itation Criteria and Procedures [4]: ‘Engineering design integrates mathematics, basic sciences, engi-
neering sciences and complementary studies in developing elements, systems and processes to meet
specific needs. It is a creative, iterative and often open-ended process subject to constraints....’While
not strong on the complementary aspect, the projects are strong on the creative, iterative, open-ended,
and subject-to-constraints aspects.
Outline of the content of the remaining sections
First, types of QR mechanisms and potential techniques for their synthesis are
reviewed. The subsequent section presents a typical set of requirements for the QR
project. Note that the project requires application of analysis techniques taught very
early within a first course on the theory of mechanisms, requires the development
of relevant synthesis techniques, and exposes students to the application of
computer-based algorithms for the analysis of mechanisms. Examples of solution
techniques that have been used to solve portions of the QR project are then pre-
sented. The paper closes with further considerations and conclusions.
Quick-return mechanism types and synthesis techniques
Example QR mechanisms
Consider the offset slider-crank illustrated in Fig. 1a. The crank (member 2) is rotat-
ing clockwise and rotates a displacement a(B¢to B≤) as the piston, C, moves from
C¢(top-dead-centre, TDC) to C≤(bottom-dead-centre, BDC). As the piston moves
from BDC to TDC the crank rotates a displacement b(B≤to B¢). The time ratio (TR)
is given by:
(1)
A crank-shaper is comprised of a tool driven by an inverted slider-crank. The
crank length of a crank-shaper is less than the base length (O2to O4) of the mech-
anism. Fig. 1b illustrates a typical configuration. Notice that the crank (member 2)
is rotating counter-clock wise in this case and that the follower (member 4) of the
driving mechanism (the inverted slider-crank) oscillates between two extremes. The
crank displacements at these extremes define the values of aand bfor the device’s
TR.
A Whitworth mechanism (Fig. 1c) is formed when the crank of the slider-crank
inversion is greater than the base distance. Fig. 1c illustrates a Whitworth QR mech-
anism, where again the crank (member 2) is rotating counter-clockwise. Notice that
the follower (member 4) of the Whitworth is dragged through a full rotation during
a revolution of the crank. The crank displacements when the follower is parallel to
the sliding direction (horizontal in Fig. 1c) define the values of aand b.
Fig. 2a shows a piston being driven by the follower of a crank-rocker four-bar
linkage. From the oscillation extremes of the follower, the crank positions B¢to B≤
are defined. Fig. 2b depicts a QR mechanism driven by a drag-link (also known as
a crank-crank) linkage. The extreme positions of the piston occur when the follower
direction is parallel to the sliding direction (horizontal in Fig. 2b).
Design of QR mechanisms
After choosing a mechanism type, appropriate dimensions for the desired task must
be selected. Several techniques can be applied. The most basic techniques are physi-
cal modelling and graphical. In physical modelling, a scale model (e.g. a ‘cardboard
and pin’ model) is made and the output for a given input is directly measured. The
graphical technique involves drawing the mechanism in its various positions.
TR =ab
Quick-return mechanisms 103
International Journal of Mechanical Engineering Education 32/2
104 R. P. Podhorodeski et al.
International Journal of Mechanical Engineering Education 32/2
Physical modelling and graphical solutions are time consuming and can be inac-
curate. An alternative is to derive analytical expressions for the mechanism lengths
required for a desired TR. Note, however, that it is not always possible to derive a
closed-form solution for link lengths as a function of a desired TR, due to the non-
linear from of the TR solution. However, if a closed-form solution for the displace-
ments of the driving mechanism can be found, a solution of the TR for given link
lengths can be found iteratively. Searching over the feasible link lengths allows
mechanisms having desired TRs to be resolved.
An example quick-return project
The idea of this project is to expose students to concepts of mechanism synthesis
and to provide a practical problem where analytical, graphical, and computer-aided
analysis techniques can be applied. An example project problem, for designing a
drag-link-based QR mechanism, is given below. Available for this project are two
mechanism analysis programs: GNLINK [5], a program developed at the Univer-
sity of Manitoba and the University of Toronto, and the commercial program
Working Model®[6].
It should be noted that any QR mechanism type can be substituted for the pre-
sented drag-link-based one. Substituting different mechanism types allows the teach-
ing objectives of the project to remain the same, but allows for modification of the
project from year to year.
Example problem background
An application requires a QR mechanism with TR =1.500 and a stroke of 0.300 m.
Currently a drag-link-based QR mechanism exists, as illustrated in Fig. 3. The
current lengths of the drag-link mechanism are: distance between fixed centres O2
and O4=r1=0.1000 m, length of crank O2A=r2=0.2250 m, length of coupler AB
=r3=0.3000 m, and length of follower O4B =r4=0.2750m. The length of the slider’s
coupler is CD =r6=0.3000 m and it is connected a distance O4C =r5=0.1000 m
from O4.
The current drag-link crank and follower are made of cast iron and would be
expensive to modify. It is proposed to design a new coupler, AB (length r3), for the
four-bar and to relocate pin C (length r5) on the follower to create a mechanism
capable of performing the task requirements. Furthermore, it is suggested that the
coupler should be adjustable in length for future modification of the drag-link-based
QR for other TRs.
Fig. 3 Layout of drag-link QR mechanism.
Quick-return mechanisms 105
International Journal of Mechanical Engineering Education 32/2
Example project requirements
Design
(1) Determine a coupler link length (r3) and C pin location (r5) satisfying a TR =
1.500 and stroke =0.3000 m while maintaining the other current link lengths.
(2) Determine the range of (r3) that the adjustable coupler should accommodate to
allow the maximum number of drag-link-based TRs to be created.
Discussion issues
(1) How many mechanisms providing a specific TR are possible if only r3is varied?
(2) What is the range of TR that would be possible by adjusting the length of the
coupler?
(3) How many feasible mechanism solutions would exist for a given TR if both
the base length, O2O4, and the coupler length could be changed?
(4) Discuss the issues you would consider in the isolation of a unique mechanism
design.
Analysis
For the mechanism with TR =1.500 and stroke =0.3000 m:
(1) Evaluate the velocity and acceleration of the slider when q2=60 °, using rela-
tive motion analysis (polygons). Use w2=10.0 rad/s and a2=0.0 rad/s2for this
analysis.
(2) Check this result using the program GNLINK or Working Model®.
(3) Simulate the mechanism for a complete revolution of the input crank.
Examples of quick-return project solutions
Examples of solutions for various portions of the problem set out above are given
in this section. The solutions presented are examples of various ways that past stu-
dents have solved portions of the project.
TR and stroke solutions for known link lengths
The TDC and BDC positions of the piston occur when the follower of the drag-link
four-bar mechanism is aligned with the sliding direction. Fig. 4 illustrates these two
positions. The following equations can be derived using cosine law:
Fig. 4 Drag-link mechanism at TDC and BDC.
(2a)
(2b)
Solving for q2a and q2b in the expressions for TDC and for BDC yields:
(3a)
(3b)
In terms of q2a and q2b, the duration of the working stroke is:
(4)
Since b=2p-a, the TR can be found as:
(5)
The stroke of the drag-link-driven QR mechanism is double the length O4C, i.e.,
stroke =2*O4C. For the desired stroke of 0.3000m, O4C =0.1500 m.
Iterative solution for the value of r3
Equation (5), combined with equations (3a) and (3b), is a solution for the TR of the
device for known link lengths. For the project problem, the feasible range of r3can
be found considering Grashof’s criteria [7] for a drag-link four-bar, i.e.:
(6)
where rshort and rlong are the lengths of the shortest and the longest links, raand rbare
the lengths of the other two links, and r1is the length between the base pins [1–3].
For the given length values, rlong will be equal to either r3or r4. With r3=rlong, sub-
stituting the known length values into equation (6) yields 0.1 +r30.2250 +0.2750
and therefore r30.40. Similarly, r4=rlong yields 0.1 +0.2750 0.2250 +r3and
therefore 0.15 £r3. In summary, for the given values of r1, r2, and r4, values of r3in
the range 0.1500 m £r3£0.4000 m yield drag-link mechanisms.
Analysis of the values of the TR over the feasible r3range using the given values
of r1=0.1000 m, r2=0.2250 m, r4=0.2750 m yields the TR values illustrated in
Fig. 5. Searching the TR data used to create Fig. 5, two values, r3=0.154 m and
r3=0.250 m, are found to yield the desired TR =1.500. Again, examination of
the data indicates that TR values ranging 1.430 TR £5.538 can be achieved,
depending on the value of r3. For a desired TR, there are either zero, one, or two
feasible solutions for r3.
Analytical solution for the value of r3
Solving for q2b in terms of q2a and TR from equation (5) gives:
(7)
with fbeing equal to (TR -1)p/(TR +1).
qq pqf
22 2
1
1
ba a
=+ -
()
+=+
TR
TR
r r r r and r r
short long a b short 1
+£+ =
TR ==
-+
+-
a
b
pq q
pq q
22
22
ab
ab
apq q=- +
22ab
q2
1
2
2
41
2
3
2
24 1
2
brrr r rrr=+-
()
-
()
-
()
()
()
-
cos
q2
1
2
2
41
2
3
2
24 1
2
arrr r rrr=++
()
-
()
+
()
()
()
-
cos
For BDC: r r r r r r r b3
2
2
2
41
2
24 1 2
2=+ -
()
--
()
()
cos q
For TDC: r r r r r r r a3
2
2
2
41
2
24 1 2
2=+ +
()
-+
()
()
cos q
106 R. P. Podhorodeski et al.
International Journal of Mechanical Engineering Education 32/2
Quick-return mechanisms 107
International Journal of Mechanical Engineering Education 32/2
Equating the right-hand sides of equations (2a) and (2b) eliminates r3and yields:
(8)
Cancelling the common r2
2term, substituting for q2b from equation (7), and group-
ing the cosine terms on the left-hand side gives:
(9)
Simplifying and using the angle sum relationship for cosine [8], equation (9)
becomes:
(10)
Letting A=(r4+r1) -(r4-r1) cos f, B=(r4-r1) sin f, and C=2r4r1/r2allows
equation (10) to be expressed as:
(11)
which has the following q2a solutions [9]:
(12)
where atan 2 (numerator, denominator) denotes a quadrant corrected arctangent
function.
From equation (11), if A2+B2>C2, two solutions for q2a can be resolved. With
q2aknown, equation (2b) can be solved for r3, i.e.:
q2222
22
aBA ABCC
=
()
±+-
()
atan atan,,
ABCcos sinqq
22aa
+=
rr rr rr
r
aaa41 2 41 2 2
41
2
2
+
()
--
()
-
[]
=cos cos cos sin sinqfqfq
22
24 1 2 24 1 2 4 1
2
41
2
rr r rr r r r r r
aa
+
()
--
()
+
()
=+
()
--
()
cos cosqqf
rrr rrr rrr rrr
ab2
2
41
2
24 1 2 2
2
41
2
24 1 2
22++
()
-+
()
()
=+-
()
--
()
()
cos cosqq
Fig. 5 TR values for feasible range of r3.
108 R. P. Podhorodeski et al.
International Journal of Mechanical Engineering Education 32/2
(13)
The negative solutions for r3can be neglected since it is physically impossible to
have a negative link length. Therefore, if A2+B2>C2, two feasible solutions for
r3can exist. The solutions for r3, however, must be tested to ensure that they satisfy
the Grashof criteria for a drag-link four-bar mechanism (Equation (6)). When
A2+B2-C2=0, there is only one solution for q2a and therefore only one potential
solution for r3. When C2>A2+B2there is no real solution for q2a and therefore
no solution for r3. Therefore, there may be zero, one, or two solutions for r3,
depending on the desired TR value.
Substituting the specified TR =1.500 and the given length values, we find
q2a =6.18° or 39.38° and r3=0.1544 m or 0.2504 m, respectively. These results
confirm the r3results found iteratively above.
Selecting the preferred value for r3
The transmission angle of a mechanism determines the effectiveness it will have in
driving its payload. An ideal transmission angle is 90°. A minimum transmission
angle of 30° has been suggested [1], as has 45° [2, 3]. In any case, higher trans-
mission angles are preferred, to prevent binding of the links.
The minimum and maximum transmission angles for a drag-link mechanism
occur when the follower is aligned with the base link, i.e., for the illustrated drag-
link-based QR mechanism the minimum/maximum transmission angles occur at
TDC and BDC. Referring to Fig. 6a, the transmission angle at TDC, gTDC, can be
resolved through cosine law, i.e.:
(14)
rr rr rrr TDC2
2
3
2
41
2
34 1
2=+ +
()
-+
()
cosg
rrrrrrr a32
2
41
2
24 1 2
2=± + +
()
-+
()
()
cos q
Fig. 6 Force transmission angles at: (a) TDC and (b) BDC.
and therefore:
(15)
Similarly, with reference to Fig. 6b, BDC yields:
(16)
giving:
(17)
The minimum transmission angle is gmin =min(gTDC, gBDC). The known link lengths
and the found values, r3=0.1544 m and 0.2504 m, yield gminr3=0.1544 =min(10.49°,
85.94°) =10.47° and gminr3=0.2504 =min(35.60°, 60.83°) =35.60°. Therefore, r3=0.2504
m is the preferred solution.
Discussion issues
(1) As seen by the TR calculations for potential r3values in Fig. 5, either zero, one,
or two r3values may exist, depending on the desired TR value.
(2) A range of TR values, 1.430 TR £5.538, exists for the range of feasible r3
lengths in drag-link mechanisms.
(3) If both the base length O2–O4and the coupler length, r3, were adjustable, a
single order of infinity of solutions would exist for a given TR.
(4) As seen in solving for the preferred value of r3, the minimum transmission
angle can be critical in the isolation of a unique mechanism design.
Analysis of the kinematics
Solving for the slider velocity
Known: q2=60°, w2=10rad/s, a2=0 rad/s2, O2A=r2=0.2250 m, AB =r3=
0.2504 m, O4B =r4=0.2750 m, O4C =r5=0.1500m, and CD =r6=0.3000m. Fig.
7a depicts the mechanism with the link lengths required to achieve a TR =1.500.
Using relative velocity analysis:
(18)
(19)
The relative velocity equations above are solved in sequence and each has two
unknown quantities. Table 1 describes the known and unknown vector components
for the equations. In Table 1 the symbol ^is used to denote perpendicular and the
symbol ? is used to denote an unknown quantity.
The unknowns may be resolved using the graphical method shown in Fig. 7b.
Table 2 summarizes the magnitudes found from Fig. 7b.
Solving for the slider acceleration
Using relative acceleration analysis:
rrr
VVV
DCDC
=+
rrr
VVV
BABA
=+
gBDC
rrr r
rr r
=+-
()
-
-
()
Ê
Ë
Áˆ
¯
˜
-
cos 13
2
41
2
2
2
34 1
2
rr rr rrr BDC2
2
3
2
41
2
34 1
2=+ -
()
--
()
cosg
gTDC
rrr r
rr r
=++
()
-
+
()
Ê
Ë
Áˆ
¯
˜
-
cos 13
2
41
2
2
2
34 1
2
Quick-return mechanisms 109
International Journal of Mechanical Engineering Education 32/2
110 R. P. Podhorodeski et al.
International Journal of Mechanical Engineering Education 32/2
(20)
(21)
The relative acceleration equations above are solved in sequence and each has
two unknown quantities. Table 3 describes the known and unknown vector com-
rrr
rr rrr r
aaa
aa aaa a
DCDC
D
n
D
t
C
n
C
t
DC
n
DC
t
=+
+=++ +
rrr
rrrrr r
aaa
aaaaa a
BABA
B
n
B
t
A
n
A
t
BA
n
BA
t
=+
+=++ +
Fig. 7 Analysis of kinematics at q2=60 °: (a) required drag-link QR mechanism, (b)
velocity polygon and (c) acceleration polygon.
TABLE 1 Known and unknown velocity components
Velocity Magnitude (m/s) Direction
A(|w2|)O2A=2.250 150 ° (i.e., ^to )
B/A ?^to
B?^to
CFound by velocity image Same direction as B
D/C ?^to
D? Horizontal (sliding direction)
r
V
DC
r
V
r
V
r
V
OB
4
r
V
AB
r
V
OA
2
r
V
Quick-return mechanisms 111
International Journal of Mechanical Engineering Education 32/2
ponents for the equations. For Table 3 it has been noted that the magnitude of t
A
is zero since a2=0 rad/s2and that the magnitude of n
Dis also zero since the piston
Dslides on a straight surface.
The unknowns may be solved for using the graphical construction shown in
Fig. 7c. Measuring from Fig. 7c, the magnitude of n
Dis 21.7 m/s2, with its direction
being to the left.
Computer-aided analysis
The drag-link-driven QR mechanism is a two-loop, single-input mechanism. Vectors
can be used to represent the mechanism’s links, as illustrated in Figure 8a. With this
model, the angular displacement, velocity, and acceleration of vector 2 are the
mechanism’s inputs.
The mechanism has been simulated on GNLINK and Working Model®. Results
from GNLINK are presented. Figure 8b shows a simulation of the mechanism
through a full rotation. Table 4 summarizes the vector model used to model the
mechanism. Table 5 presents kinematic results output for q2=60°. The results are
identical, to three significant figures, to those found graphically using AutoCAD®
above (Fig. 7).
r
a
r
a
r
a
TABLE 2 Velocity magnitudes
Velocity Magnitude (m/s)
B/A 1.898
B3.219
C1.756
D/C 1.631
D1.075
r
V
r
V
r
V
r
V
r
V
TABLE 3 Known and unknown acceleration components
Acceleration Magnitude (m/s2) Direction
n
Aw2
2*O2A=22.50 // to O2A (directed towards O2)
n
B/A || B/A||2/AB =14.39 // to (directed towards A)
t
B/A ?^to
n
B|| B||2/O4B =37.68 // to (directed towards O4)
t
B?^to
CFound by acceleration image Same direction as B
n
D/C || D/C||2/CD =8.87 // to (directed towards C)
t
D/C ?^to
t
D? Horizontal (sliding direction)
r
a
CD
r
a
CD
r
V
r
a
r
a
r
a
OB
4
r
a
OB
4
r
V
r
a
AB
r
a
AB
r
V
r
a
r
a
112 R. P. Podhorodeski et al.
International Journal of Mechanical Engineering Education 32/2
TABLE 5 GNLINK kinematic results for q2=60 °
Results are tabulated using the following format. Print out may be paused by pressing <Ctrl S>. To
start print out press <CR>.
TIME
In1 In1D In1DD Dep 1 Dep 1D Dep 1DD
Dep 2 Dep 2D Dep 2DD Dep 3 Dep 3D Dep 3DD
Dep 4 Dep 4D Dep 4DD
T=.0000E+00
.1047E+01 .1000E+02 .0000E+00 -.3247E+00 .7566E+01 -.5118E+02
.4313E+00 .1169E+02 -.4541E+02 .2931E+01 -.5430E+01 .4400E+02
.4296E+00 -.1074E+01 -.2167E+02
TABLE 4 GNLINK model of the drag-link QR mechanism
Initial Vector Information
Vector No. Length Angle
1 .1000E+00 .0000E+00
2 .2250E+00 .6000E+02
3 .2504E+00 -.3000E+02
4 .2750E+00 .3000E+02
5 .1500E+00 .3000E+02
6 .3000E+00 .1600E+03
7 .3000E+00 .0000E+00
Dependent Variables
Dependent Variable No. Vector No. A or L
13A
24A
36A
47L
Common Variable Pairs
Pair No. Primary Secondary A or L Difference
1 4 5 A .0000E+00
Loop Sequences
Loop No. Sequence
123-4-1
25-6-7
Quick-return mechanisms 113
International Journal of Mechanical Engineering Education 32/2
Further considerations
On the accuracy of the graphical velocity and acceleration solutions
The high accuracy achieved in the graphical analysis of velocity and acceleration
values is due to the use of a computer-aided drawing package. While not manda-
tory, approximately 60% of the students utilize such packages and achieve similar
accuracy.
On theory of mechanisms laboratory and the format and value of the labs
The laboratory used for the theory of mechanisms class has a reconfigurable mech-
anism testbed, which allows the construction and running of different mechanism
types, including the drag-link-based QR. In addition, the laboratory has several PC-
based computers running mechanism simulation software, including GNLINK, the
program used in this work, and CAMPRF [10] a cam-profile-design program. Also
found in the laboratory are a cut-away five-speed manual transmission and various
scales and knife edges to allow the determination of the inertia properties of links.
Students are divided into groups of three for the laboratories. Each group has
access to the laboratory for approximately one hour per week. Over the 13 weeks
of the term, students are currently scheduled to complete the following four lab
projects:
(1) Design and analysis of a QR mechanism.
(2) Approximate modelling and physical determination of inertia properties.
Fig. 8 GNLINK results: (a) vector model of the drag-link QR mechanism, (b) motion
simulation of the mechanism.
(3) Design and analysis of cam and follower systems.
(4) Observation and calculation of gear reduction ratios.
The timing of the specific projects coincides with the material coverage in the course.
On the manual for the QR project
The laboratory manual for the QR project basically consists of the information found
within the introductory sections to this paper. While the background remains the
same, the type of mechanism featured in the project varies from year to year.
Conclusions
Having a project related to QR mechanism design and analysis is very beneficial to
the students. The experience familiarizes the students with the terminology of mech-
anisms, with concepts related to mechanism synthesis, with relative motion analy-
sis, and with techniques and computer programs for the design and analysis of
mechanisms. Since the task of a QR mechanism and the kinematic analysis involved
in the project are basic, the project functions very well within the first four weeks
of a first course on the theory of mechanisms to strengthen student understanding
of the taught material.
Acknowledgement
The undergraduate students of the Department of Mechanical Engineering, Univer-
sity of Victoria, are thanked for providing effective feedback on the QR mechanism
project.
References
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[4] Canadian Engineering Accreditation Board (CEAB), Accreditation Criteria and Procedures
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V1–V7.
[6] Knowledge Revolution, Working Model 2D – User’s Manual (1996).
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ON, 1986).
[10] W. L. Cleghorn and R. P. Podhorodeski, ‘Disc cam design using a microcomputer’, Int. J. Mech.
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114 R. P. Podhorodeski et al.
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