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  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 ﬁrst. 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 mechanisms 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 determination 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 mechanism 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 combinations (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
  International Journal of Mechanical Engineering Education 32/2
  The task of a QR mechanism is simple to understand. etc. for example. mechanisms of various types and/or dimensions that satisfy the primary task exist. of minimum transmission angles. physical modelling. iterative.Quick-return mechanisms 101 Fig. Several techniques can be considered and developed by students to achieve the required synthesis task. Having a laboratory manual that brieﬂy outlines different possible techniques.. and leaves the International Journal of Mechanical Engineering Education 32/2 . For example. graphical. minimum transmission angles. can be considered to isolate a preferred design. Several concepts of design and analysis can be illustrated by a QR mechanism project. (b) crank-shaper. of type and dimensional synthesis. and of computer-aided modelling programs. and analytical techniques can all be used to synthesize a desired mechanism. students can be exposed to concepts of kinematic analysis. (c) Whitworth. maximum accelerations. concerns such as mechanism size. 1 Slider-crank QR mechanisms: (a) offset slider-crank.
  AUs are assigned to the curriculum content of the courses within the program under consideration. Podhorodeski et al. and has allowed the assignment to the course of a signiﬁcant percentage of accreditation units (AUs) for Engineering design [4]. student-applied technique open.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. (b) draglink (crank-crank) as the driving mechanism. requires a creative algorithm-design process. the projects are strong on the creative. . Over the past 10 years at the Department of Mechanical Engineering. iterative and often open-ended process subject to constraints. It is a creative. basic sciences. (d) engineering design. This course occurs in the ﬁrst term of third year. systems and processes to meet speciﬁc needs. along with similar technique-open projects on inertia modelling and on cam design. engineering sciences and complementary studies in developing elements. and subject-to-constraints aspects. Fig. has given the students a strong appreciation of mechanism analysis and design issues. P.’ While not strong on the complementary aspect. International Journal of Mechanical Engineering Education 32/2 . a variety of projects featuring different mechanism types have been used within a ﬁrst course on the theory of mechanisms. 1 The Canadian Engineering Accreditation Board (CEAB) performs accreditation of all undergraduate engineering programmes in Canada. open-ended. (b) basic sciences. Currently AUs are divided between (a) mathematics. 2 Four-bar QR mechanisms: (a) crank-rocker as the driving mechanism. Quoting CEAB Accreditation Criteria and Procedures [4]: ‘Engineering design integrates mathematics. The QR project.102 R. . of a semestered four-year academic programme that leads to an accredited bachelor of engineering in mechanical engineering degree. iterative. . University of Victoria. and (e) complementary studies. (c) engineering sciences.
  2b depicts a QR mechanism driven by a drag-link (also known as a crank-crank) linkage.Quick-return mechanisms 103 Outline of the content of the remaining sections First. 1b illustrates a typical conﬁguration. 2a shows a piston being driven by the follower of a crank-rocker four-bar linkage. Quick-return mechanism types and synthesis techniques Example QR mechanisms Consider the offset slider-crank illustrated in Fig. a ‘cardboard and pin’ model) is made and the output for a given input is directly measured. Fig. Design of QR mechanisms After choosing a mechanism type. 1c) is formed when the crank of the slider-crank inversion is greater than the base distance. Note that the project requires application of analysis techniques taught very early within a ﬁrst course on the theory of mechanisms. BDC). The subsequent section presents a typical set of requirements for the QR project. The crank length of a crank-shaper is less than the base length (O2 to O4) of the mechanism. types of QR mechanisms and potential techniques for their synthesis are reviewed. a scale model (e.g. Fig. Several techniques can be applied. appropriate dimensions for the desired task must be selected. requires the development of relevant synthesis techniques. moves from C¢ (top-dead-centre. where again the crank (member 2) is rotating counter-clockwise. From the oscillation extremes of the follower. The time ratio (TR) is given by: TR = a b (1) A crank-shaper is comprised of a tool driven by an inverted slider-crank. Examples of solution techniques that have been used to solve portions of the QR project are then presented. TDC) to C≤ (bottom-dead-centre. Notice that the follower (member 4) of the Whitworth is dragged through a full rotation during a revolution of the crank. Fig. 1c) deﬁne the values of a and b. 2b). C. The crank displacements when the follower is parallel to the sliding direction (horizontal in Fig. 1c illustrates a Whitworth QR mechanism. 1a. As the piston moves from BDC to TDC the crank rotates a displacement b (B≤ to B¢). the crank positions B¢ to B≤ are deﬁned. The graphical technique involves drawing the mechanism in its various positions. A Whitworth mechanism (Fig. The most basic techniques are physical modelling and graphical. The extreme positions of the piston occur when the follower direction is parallel to the sliding direction (horizontal in Fig. and exposes students to the application of computer-based algorithms for the analysis of mechanisms. The crank displacements at these extremes deﬁne the values of a and b for the device’s TR. In physical modelling. The crank (member 2) is rotating clockwise and rotates a displacement a (B¢ to B≤) as the piston. International Journal of Mechanical Engineering Education 32/2 . The paper closes with further considerations and conclusions. Fig. 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.
  1000 m. for the four-bar and to relocate pin C (length r5) on the follower to create a mechanism capable of performing the task requirements. 3. However.104 R. that it is not always possible to derive a closed-form solution for link lengths as a function of a desired TR. The length of the slider’s coupler is CD = r6 = 0. Furthermore.3000 m. however. An alternative is to derive analytical expressions for the mechanism lengths required for a desired TR. 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. 3 Layout of drag-link QR mechanism. but allows for modiﬁcation of the project from year to year. if a closed-form solution for the displacements of the driving mechanism can be found. It should be noted that any QR mechanism type can be substituted for the presented drag-link-based one. a solution of the TR for given link lengths can be found iteratively. graphical. Example problem background An application requires a QR mechanism with TR = 1. Searching over the feasible link lengths allows mechanisms having desired TRs to be resolved.2750 m. An example project problem.2250 m. and length of follower O4B = r4 = 0.300 m. Podhorodeski et al. The current lengths of the drag-link mechanism are: distance between ﬁxed centres O2 and O4 = r1 = 0. length of coupler AB = r3 = 0. It is proposed to design a new coupler.1000 m from O4. P. due to the nonlinear from of the TR solution. and the commercial program Working Model® [6]. it is suggested that the coupler should be adjustable in length for future modiﬁcation of the drag-link-based QR for other TRs. for designing a drag-link-based QR mechanism. is given below. a program developed at the University of Manitoba and the University of Toronto. International Journal of Mechanical Engineering Education 32/2 .3000 m and it is connected a distance O4C = r5 = 0. The current drag-link crank and follower are made of cast iron and would be expensive to modify.500 and a stroke of 0. AB (length r3). length of crank O2A = r2 = 0. Currently a drag-link-based QR mechanism exists. as illustrated in Fig. Substituting different mechanism types allows the teaching objectives of the project to remain the same. Note. and computer-aided analysis techniques can be applied. Available for this project are two mechanism analysis programs: GNLINK [5]. Physical modelling and graphical solutions are time consuming and can be inaccurate. Fig.
  Quick-return mechanisms 105 Example project requirements Design (1) Determine a coupler link length (r3) and C pin location (r5) satisfying a TR = 1.500 and stroke = 0.500 and stroke = 0. 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. The following equations can be derived using cosine law: Fig. 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. using relative motion analysis (polygons).3000 m while maintaining the other current link lengths. International Journal of Mechanical Engineering Education 32/2 . Fig.0 rad/s2 for this analysis. The solutions presented are examples of various ways that past students have solved portions of the project.0 rad/s and a2 = 0. Use w2 = 10. (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. (3) Simulate the mechanism for a complete revolution of the input crank. 4 illustrates these two positions. Examples of quick-return project solutions Examples of solutions for various portions of the problem set out above are given in this section. O2O4.3000 m: (1) Evaluate the velocity and acceleration of the slider when q2 = 60 °. 4 Drag-link mechanism at TDC and BDC. (2) Check this result using the program GNLINK or Working Model®. Discussion issues (1) How many mechanisms providing a speciﬁc TR are possible if only r3 is 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.
  depending on the value of r3.: rshort + rlong £ ra + rb and rshort = r1 (6) where rshort and rlong are the lengths of the shortest and the longest links. For TDC: r 2 = r 2 + (r4 + r1 ) . In summary. the feasible range of r3 can be found considering Grashof’s criteria [7] for a drag-link four-bar.1)p = q 2a + f TR + 1 (7) with f being equal to (TR .2250 + r3 and therefore 0. examination of the data indicates that TR values ranging 1. i. O4C = 0. i.q 2a + q 2 b = b p + q 2a . one.2250 m. 5.1000 m.r1 ) .1 + r3 0.2 r2 (r4 . Similarly.2750 0. Analysis of the values of the TR over the feasible r3 range using the given values of r1 = 0. For the project problem. stroke = 2 * O4C.. r2. there are either zero.1 + 0.e.r1 ) cos(q 2 b ) 2 3 2 2 2 2 (2a) (2b) Solving for q2a and q2b in the expressions for TDC and for BDC yields: q 2 a = cos -1 (r 2 + (r4 + r1 ) . is a solution for the TR of the device for known link lengths. Iterative solution for the value of r3 Equation (5).r 2 ) (2 r2 (r4 3 2 ) .2750 m yields the TR values illustrated in Fig.250 m. combined with equations (3a) and (3b). the duration of the working stroke is: a = p .r 2 ) (2 r2 (r4 + r1 )) 2 3 2 q 2 b = cos -1 ( ((r 2 2 + (r4 . For the given length values.538 can be achieved.a.106 R. For a desired TR. Podhorodeski et al.q 2a + q 2 b Since b = 2p .2 r2 (r4 + r1 ) cos(q 2 a ) 3 2 For BDC: r = r + (r4 .15 £ r3.500. r2 = 0. Searching the TR data used to create Fig. rlong will be equal to either r3 or r4. r4 = 0.2250 + 0.e. for the given values of r1.2750 and therefore r3 0.r1 ) .q 2 b (5) (4) The stroke of the drag-link-driven QR mechanism is double the length O4C.1500 m £ r3 £ 0. With r3 = rlong.3000 m. and r1 is the length between the base pins [1–3]. two values. r3 = 0. the TR can be found as: TR = a p . P. Analytical solution for the value of r3 Solving for q2b in terms of q2a and TR from equation (5) gives: q 2 b = q 2a + (TR .1500 m. 5.154 m and r3 = 0.r ))) 1 (3a) (3b) In terms of q2a and q2b. r4 = rlong yields 0.4000 m yield drag-link mechanisms.430 TR £ 5. or two feasible solutions for r3.1)p/(TR + 1). are found to yield the desired TR = 1.40. ra and rb are the lengths of the other two links. International Journal of Mechanical Engineering Education 32/2 . Again. and r4. substituting the known length values into equation (6) yields 0. values of r3 in the range 0. For the desired stroke of 0.
  2 r2 (r4 + r1 ) cos(q 2 a ) = r 2 + (r4 .2 r2 (r4 .sin f sin q 2 a ] = 2 r4 r1 r2 (10) Letting A = (r4 + r1) . B = (r4 .: International Journal of Mechanical Engineering Education 32/2 . and C = 2r4r1/r2 allows equation (10) to be expressed as: A cos q 2 a + B sin q 2 a = C which has the following q2a solutions [9]: q 2 a = atan 2(B.Quick-return mechanisms 107 Fig. With q2a known.r1 ) cos(q 2 b ) 2 2 2 2 (8) Cancelling the common r22 term. Equating the right-hand sides of equations (2a) and (2b) eliminates r3 and yields: r 2 + (r4 + r1 ) .r1) sin f. two solutions for q2a can be resolved.(r4 .C 2.r1 )[cos f cosq 2 a .2 r2 (r4 . equation (2b) can be solved for r3. From equation (11). 5 TR values for feasible range of r3.(r4 .r1) cos f.e.r1 ) . substituting for q2b from equation (7). A) ± atan 2( A 2 + B 2 . C) (12) (11) where atan 2 (numerator.(r4 . i. if A2 + B2 > C2. equation (9) becomes: (r4 + r1 ) cosq 2 a .r1 ) 2 2 (9) Simplifying and using the angle sum relationship for cosine [8].r1 ) cos(q 2 a + f ) = (r4 + r1 ) . and grouping the cosine terms on the left-hand side gives: 2 r2 (r4 + r1 ) cos q 2 a . denominator) denotes a quadrant corrected arctangent function.
  one. 6 Force transmission angles at: (a) TDC and (b) BDC. depending on the desired TR value. r3 = ± r 2 + (r4 + r1 )2 . i. to prevent binding of the links.2504 m. The minimum and maximum transmission angles for a drag-link mechanism occur when the follower is aligned with the base link.C2 = 0. there is only one solution for q2a and therefore only one potential solution for r3. 6a.500 and the given length values. A minimum transmission angle of 30° has been suggested [1].18° or 39.e. for the illustrated draglink-based QR mechanism the minimum/maximum transmission angles occur at TDC and BDC.: r 2 = r 2 + (r4 + r1 ) . Referring to Fig.1544 m or 0. An ideal transmission angle is 90°. These results conﬁrm the r3 results found iteratively above..2 r3 (r4 + r1 ) cosg TDC 2 3 2 (14) Fig. respectively. P. Selecting the preferred value for r3 The transmission angle of a mechanism determines the effectiveness it will have in driving its payload.38° and r3 = 0. gTDC. or two solutions for r3. i. When C2 > A2 + B2 there is no real solution for q2a and therefore no solution for r3. Therefore.108 R. The solutions for r3. Therefore. if A2 + B2 > C2. however. higher transmission angles are preferred. International Journal of Mechanical Engineering Education 32/2 . In any case. there may be zero. When A2 + B2 . can be resolved through cosine law. two feasible solutions for r3 can exist. Substituting the speciﬁed TR = 1.2 r2 (r4 + r1 ) cos(q 2 a ) 2 (13) The negative solutions for r3 can be neglected since it is physically impossible to have a negative link length. as has 45° [2. must be tested to ensure that they satisfy the Grashof criteria for a drag-link four-bar mechanism (Equation (6)).e. Podhorodeski et al. 3]. the transmission angle at TDC. we ﬁnd q2a = 6.
  Using relative velocity analysis: r r r (18) VB = VA + VB A r r r (19) VD = VC + VD C The relative velocity equations above are solved in sequence and each has two unknown quantities. (4) As seen in solving for the preferred value of r3. O4B = r4 = 0. exists for the range of feasible r3 lengths in drag-link mechanisms. either zero.1544 = min(10. r3 = 0. w2 = 10 rad/s.49°. BDC yields: r 2 = r 2 + (r4 . yield gminr3=0. Therefore. were adjustable. a single order of inﬁnity of solutions would exist for a given TR. a2 = 0 rad/s2.47° and gminr3=0. 5. O2A = r2 = 0.2750 m. 7a depicts the mechanism with the link lengths required to achieve a TR = 1.94°) = 10. 7b.2504 m. (3) If both the base length O2–O4 and the coupler length. Table 2 summarizes the magnitudes found from Fig. 60. one. gBDC). 1.430 TR £ 5. The unknowns may be resolved using the graphical method shown in Fig. Discussion issues (1) As seen by the TR calculations for potential r3 values in Fig.3000 m.Quick-return mechanisms 109 and therefore: Ê r 2 + (r4 + r1 )2 .538.60°.60°. Solving for the slider acceleration Using relative acceleration analysis: International Journal of Mechanical Engineering Education 32/2 . The known link lengths and the found values.2504 m is the preferred solution.2 r3 (r4 . r3. the minimum transmission angle can be critical in the isolation of a unique mechanism design. depending on the desired TR value. with reference to Fig.r 2 ˆ 3 2 g TDC = cos -1 Á ˜ 2 r3 (r4 + r1 ) ¯ Ë Similarly.r1 ) cosg BDC 2 3 giving: Ê r 2 + (r4 .83°) = 35. O4C = r5 = 0.1544 m and 0.r1 ) ¯ Ë (17) 2 (15) (16) The minimum transmission angle is gmin = min(gTDC.2504 = min(35. Analysis of the kinematics Solving for the slider velocity Known: q2 = 60°.2504 m. Table 1 describes the known and unknown vector components for the equations. r3 = 0. and CD = r6 = 0. Fig.500.r 2 ˆ 3 2 g BDC = cos -1 Á ˜ 2 r3 (r4 . AB = r3 = 0.r1 ) . or two r3 values may exist. In Table 1 the symbol ^ is used to denote perpendicular and the symbol ? is used to denote an unknown quantity. (2) A range of TR values. 7b.1500 m.2250 m.r1 )2 . 6b. 85.
  . Table 3 describes the known and unknown vector comInternational Journal of Mechanical Engineering Education 32/2 . ^ to O 2 A) ^ to AB ^ to O 4 B r Same direction as VB ^ to DC Horizontal (sliding direction) Velocity r VA r VB/A r VB r VC r VD/C r VD Magnitude (m/s) (|w2|)O2A = 2.110 R. P. Podhorodeski et al.250 ? ? Found by velocity image ? ? r aB rn rt aB + aB r aD rn rt aD + aD r r = aA + aB A rn r rn rt = a A + a tA + a B A + a B A r r = aC + aD C rn rt rn rt = aC + aC + aD C + aD C (20) (21) The relative acceleration equations above are solved in sequence and each has two unknown quantities. TABLE 1 Known and unknown velocity components Direction 150 ° (i.e. Fig. (b) velocity polygon and (c) acceleration polygon. 7 Analysis of kinematics at q2 = 60 °: (a) required drag-link QR mechanism.
  and acceleration of vector 2 are the mechanism’s inputs. the magnitude of an is 21. to those found graphically using AutoCAD® above (Fig.7 m/s2. 7). to three signiﬁcant ﬁgures. International Journal of Mechanical Engineering Education 32/2 .68 r aB // to CD (directed towards C) r ponents for the equations. For Table 3 it has been noted that the magnitude of atA rn is zero since a2 = 0 rad/s2 and that the magnitude of aD is also zero since the piston D slides on a straight surface. 7c. the angular displacement. Measuring from Fig. Computer-aided analysis The drag-link-driven QR mechanism is a two-loop. velocity. Results from GNLINK are presented.39 ? ? Found by acceleration image r || VD/C||2/CD = 8.Quick-return mechanisms 111 TABLE 2 Velocity r VB/A r VB r VC r VD/C r VD Velocity magnitudes Magnitude (m/s) 1.898 3. With this model.631 1. single-input mechanism. 7c. as illustrated in Figure 8a.075 TABLE 3 Acceleration Known and unknown acceleration components Magnitude (m/s2) Direction // to O2A (directed towards O2) // to AB (directed towards A) ^ to AB // to O 4 B (directed towards O4) ^ to O 4 B Same direction as ^ to CD Horizontal (sliding direction) rn aA r an r B/A t a B/A rn aB rt aB r aC r an r D/C t a D/C rt aD w2 * O2A = 22. with its direction D being to the left. Figure 8b shows a simulation of the mechanism through a full rotation. The unknowns may be solved for using the graphical construction shown in r Fig. Vectors can be used to represent the mechanism’s links.756 1.50 2 r || VB/A||2/AB = 14. Table 5 presents kinematic results output for q2 = 60°.219 1. The results are identical. The mechanism has been simulated on GNLINK and Working Model®. Table 4 summarizes the vector model used to model the mechanism.87 ? ? r || VB||2/O4B = 37.
  5430E+01 -.7566E+01 -. 1 2 Primary 4 GNLINK model of the drag-link QR mechanism Length .5118E+02 .1500E+00 .4313E+00 . 1 Loop Sequences Loop No.4541E+02 -.1047E+01 .4296E+00 In1D Dep 2D Dep 4D . Podhorodeski et al.6000E+02 -.3247E+00 .0000E+00 .2931E+01 .0000E+00 Vector No. 3 4 6 7 A or L A A A L Secondary 5 A or L A Difference .3000E+00 Angle .112 R. TABLE 4 Initial Vector Information Vector No. P.3000E+02 .3000E+02 .1000E+00 .2750E+00 .1169E+02 -. TIME In1 Dep 2 Dep 4 T = . 1 2 3 4 Common Variable Pairs Pair No. 1 2 3 4 5 6 7 Dependent Variables Dependent Variable No.3000E+00 .0000E+00 . Print out may be paused by pressing <Ctrl S>.0000E+00 Sequence 2 5 3 -6 -4 -7 -1 TABLE 5 GNLINK kinematic results for q2 = 60 ° Results are tabulated using the following format.1600E+03 .3000E+02 .2250E+00 .1074E+01 In1DD Dep 2DD Dep 4DD .2504E+00 .2167E+02 Dep 1 Dep 3 Dep 1D Dep 3D Dep 1DD Dep 3DD -. To start print out press <CR>.4400E+02 International Journal of Mechanical Engineering Education 32/2 .1000E+02 .0000E+00 -.
  and CAMPRF [10] a cam-proﬁle-design program. approximately 60% of the students utilize such packages and achieve similar accuracy. students are currently scheduled to complete the following four lab projects: (1) (2) Design and analysis of a QR mechanism. including the drag-link-based QR. which allows the construction and running of different mechanism types. 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. the program used in this work. In addition. including GNLINK. 8 GNLINK results: (a) vector model of the drag-link QR mechanism. While not mandatory. Over the 13 weeks of the term. the laboratory has several PCbased computers running mechanism simulation software. 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. Each group has access to the laboratory for approximately one hour per week. 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 mechanism testbed.Quick-return mechanisms 113 Fig. (b) motion simulation of the mechanism. International Journal of Mechanical Engineering Education 32/2 . Approximate modelling and physical determination of inertia properties. Students are divided into groups of three for the laboratories.
  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. Theory of Machines and Mechanisms. [10] W. Proc. J. ‘Disc cam design using a microcomputer’. Erdman and G. Since the task of a QR mechanism and the kinematic analysis involved in the project are basic. Uicker. Toronto. Don Mills. G. Podhorodeski et al. Cleghorn. [8] D. Conclusions Having a project related to QR mechanism design and analysis is very beneﬁcial to the students. Podhorodeski and W. The timing of the speciﬁc projects coincides with the material coverage in the course. Educ. 30th edn (CRC Press. A. of the 9th Applied Mechanism Conference (Kansas City. 1996). Accreditation Criteria and Procedures (Canadian Council of Professional Engineers. ‘Multiple-loop mechanism analysis using a microcomputer’. Introduction to Robotics – Mechanics and Control. pp. International Journal of Mechanical Engineering Education 32/2 . Podhorodeski. While the background remains the same. The experience familiarizes the students with the terminology of mechanisms. 1987). Mabie and C. 1997). MO. Motion Geometry of Mechanisms (Cambridge University Press. Dijksman. NJ. 1986). ON. [4] Canadian Engineering Accreditation Board (CEAB). Working Model 2D – User’s Manual (1996). L. 4th edn (John Wiley & Sons..114 R. E. 235–250. 2nd edn (Addison-Wesley. Mechanism Design – Analysis and Synthesis. Craig. University of Victoria. H. 2000). [6] Knowledge Revolution. [5] R. New York. New York. October 1985). 1995). CRC Standard Mathematical Tables and Formulae. Mechanics and Dynamics of Machinery. [7] E. 1976). V1–V7. with concepts related to mechanism synthesis. P. Shigley and J. Enging. Jr. and with techniques and computer programs for the design and analysis of mechanisms. 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. Reinholtz. (3) (4) Design and analysis of cam and follower systems. 3rd edn (Prentice Hall. [9] J. References [1] A. 2nd edn (McGraw-Hill. P. S. Sandor. with relative motion analysis. Upper Saddle River. J. Mech. 16(4) (1988). ed. L. Acknowledgement The undergraduate students of the Department of Mechanical Engineering. P. F. are thanked for providing effective feedback on the QR mechanism project. Cleghorn and R. [3] H. Toronto. Zwillinger. Observation and calculation of gear reduction ratios. [2] J. the type of mechanism featured in the project varies from year to year. Int.. J.