Homework 4 PROBLEMS ON THREE POSITION GUIDANCE

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1 Homework 4 ROLEMS ON THREE OSITION GUIDNE. In the synthesis of three positions of a plane by a four-bar mechanism, in the graphical method and were selected arbitrarily and, were determined as the corresponding centerpoints. Determine the procedure of selecting, arbitrarily. Where will be,. (Hint: onsider the motion inverted, fixed plane moving and the moving plane fixed. What will happen to the poles? What is in this inverted motion? What is?).. rigid body in plane motion is shown in three positions. a) Locate the poles and draw the pole triangle. b) Locate the point on the moving system which has its three positions on a circular arc about D (,-7) as the center (Locate D ) c) Locate the locus of points on the moving system having their three corresponding positions on a straight line. (.Hall) (,5) (,) (,) (7,) (,). positions of a link given below: Determine the proportions of the following mechanisms which are to synthesize this motion and draw the mechanisms in position #. a) Link is guided by two pins fitting into straight guides. b) Link isguided on the planet gear of an epicyclic gear train, in which the sun and planet gears have the same number of teeth. (External mesh) c) Link is attached to the coupler link of a 4-bar mechanism. (,) (,) (,) Es/es.5.

2 4. Line g (shown as g at position # ) belongs to a body moved through three positions, the pole triangle being as shown. Find g and g by the most direct construction you can devise. (you can select any two points on g and determine their corresponding positions hence determine g, g but try to find another method.) g 5. Three positions of a body in plane motion is specified. ositions and coincide. For two points and, velocity directions are given in position (or ). an the pole triangle be drawn? an you construct a four-bar mechanism to realize this motion. How would you formulate this problem by utilizing the dyad formulation? 6. four-link, planar RR mechanism is shown below. (This mechanism is known as conchoidal motion mechanism). Synthesize the proportions of this mechanism for the following displacements: φ =, φ = (W), φ = 6 (W), = (,), = (, mm) and the direction of the motion of the slider is to be parallel to the direction of. Verify your solution by drawing the mechanism in all positions. R 4 R Es/es.5.

3 7. mechanically reproduced scooping motion incorporated in a truck designed principally for handling lead are is shoun. It is required to determine the follower ( ) positon. referably, we would like to have withing the region enclosed in dotted lines and on the line = 55 mm = 55 mm. 6 R We would like to replace the slider guidance of the slider crank mechanism by a follower ( ) attached to the coupler for the positions shown. is to be the crank for this 4-bar mechanism, and we would like to have crank-rocker proportions. Determine a follower ( =5, =). Es/es.5.

4 9. Figure shows the thread feed of a central spool sewing machine. The eye of the thread lever has to be on the lines l, l, l when the crank rotates by angles θ and θ. Originally, the motion was achieved by a disk cam. four-bar mechanism was found to be more advantageous. Since the first and the third positions must be at the dead center positions of the crank (the eye must not be above l and below ) a crank was selected and a certain length for the coupler was assumed. Due to space limitations we have to select, the center of the other crank, on the machine head. n appropriate position is shown on the figure. Determine the corresponding circle point at position # ( ) so that the coupler point on the four-bar satisfies the given motion requirements. heck whether the four-bar thus obtained is of crank-rocker proportions. If you want, you can select at another position on the machine head. (R.eyer). Es/es 4.5.

5 . Figure shows an existing slider-crank mechanism in a part of a machine ( =5, =). We would like to drive a dwell mechanism from this slider-crank mechanism. Link 6 is required to be in an approximate dwell while the crank (link ) rotates by angle φ = θ = θ +θ as shown. possible solution would be to find a point on the coupler link (,, ) whose corresponding positions lie on a straight line. The shape of the mechanism thus obtained is shown below. If the path of point corresponds with the prismatic joint deviates from this line link 6 will translate. Synthesize such a mechanism. (R.eyer) ath of c c i c k Es/es 5.5.

6 . Figure shows an existing 8-link mechanism. Link is the driven crank and link 8 is the oscillating output. However, due to bad transmission angle of the slider at position # the machine will not function properly. Instead of a slider (link 6) we would like to attach a swinging block mechanism, while keeping the characteristics of the original motion. Hence when link rotates, link 4 has its limit positions at and We determine at the midpoint of the swing. Our aim is to determine a line on link 5 whose corresponding positions are concurrent at a point while the plane of link 5 is at positions,,. Determine the mechanism thus obtained. ompare the motion of point 8 for both mechanisms. D =5 =7 =6 =5 D =8 DD = D E 6 D =7 =5 =5 =6 D =8 DD = D Es/es 6.5.

7 . The figure shows the principle of a lift truck in which the fork is guided by a linkage. The fork must move up and down in nearly rectilinear translation. Determine the dimensions of the required linkage. Note that is a four-bar linkage, and that point should have an approximate straight-line path. Link DE maintains the fork in a motion of translation: to determine this link, use three positions of accuracy for which the fork isto be exactly horizontal at ground level, halfway up and all the way up. oints and may be chosen in any convenient location within 5x5 mm rectangle. Keep in mind that the truck must have maneuverability in close quarters where the headroom is low. There are several methods to solve this problem one possible procedure is: D E,8 a) First omit link DE and the fork D. hoosen a certain link length for and (keeping in mind the pace limitations, etc.) b) oint on link must move on a vertical line. Select corresponding points of at equal distance and determine the three positions of link. c) Draw the pole triangle for the positions of. Select a certain point, and determine its center-point, or, you can select a certain center-point and use the theorem The coupler and the fixed link subtend the same angle at the pole (look at your notes). We would like to have on the, but you can omit this requirement if necessary. d) Now that you have selected, at the three positions of draw a vertical (or horizontal) line from point. This line represents the required positions of the fork. To determine the link DE we are interested in the relative motion between the fork plane and the crank. To investigate this relative motion rotate, (and the vertical line you have drawn). bout such that and will coincide with. The new positions of (,,, say) and the fork plane is the motion relative to the crank. Draw the pole triangle for this relative motion, select a point D and determine its corresponding center point (E ). (Hartenberg). Es/es 7.5.

8 . The figure shows the principle of the linkage guidance of a mixer motor. The motor must move up and down in nearly rectilinear translation. Determine the dimensions of the required linkage for positions of the motor, lowest midway and highest. Keep space limitations in mind when coosing your links. (Look at the method discussed for the fork-lift. Later we shall see another method for the synthesis of this motion)). (Hartenberg and Volmer) E D 5 4. Design an in-line slider crankmechanism so that 9 clockwise rotation of link results in a rectilinear translation of point from left to right along a line as shown. Displacement of along the line must be approximately proportional to the corresponding rotations of within the 9 interval. Use three accuracy points. heck your result (Hartenberg). Es/es 8.5.

9 5. We would like to correlate a crank displacement with a slider displacement as shown in Fig. (a). In order to achieve this, double slide mechanism shown in Fig. (b) is considered. Derive a procedure for the synthesis of such a mechanism and using this procedure, synthesize a mechanism for which: θ = s = mm θ =4 s =4 mm θ =5 s =6 mm Hint: onsider kinematic inversion (Volmer) (a) (b) D θ θ θ D s s D D s 6. Figure (a) shows a mechanism for folding sheet metals. Slider input has been found disadvantageous and a mechanism using revolute joints has been considered as shown. The input link o is to rotate for the total motion. Synthesize this mechanism. Hint: First determine corresponding positions of the plane FD. Then select (or ) and thecorresponding (or ). Determine the total swing of the link when going from position to. Design a four bar mechanism with this swing angle and the corresponding crank rotation of (Remember lt harts?). G G,F F G G F, G G,F F D D D Es/es 9.5.

10 6. We would like to design a barber s chair in which a single control arm is to actuate both the foot rest and the head rest. Use two four-bar mechanisms in series as shown in figure (b) (not to scale) think about space limitations and aesthetics. (Erdman and Sandor). θ =.5 φ = 5 ψ = 4 θ = 45 φ = 75 ψ = 7 Head Rest hair Foot Rest 7. To protect car tape (or radio) from thieves a four-bar mechanism is to be constructed to move the tape behind the glove compartment when not in use. Figure shows a cross section of the area of interest including the glove compartment and heating duct as well as the prescribed positions for the tape unit. Since there is a small accptable are for center point, center point must be selected (Erdman and Sandor). R = 55 74i φ = R = 4 6i φ = 5 R = 5 + i φ = 9 Glove ompartment R Tape layer R R Heater Duct Es/es.5.

11 8. s part of automation process, a four-bar mechanism must be designed to remove boxes from one conveyor belt and deposit to an upper conveyor belts as shown. oth the moving and fixed pivots must be located between the upper and lower conveyor belts. a) Design a four-bar mechanism usıng graphical method. b) Design a four-bar mechanism by using the basic form of the dyad equation (specify the crank rotations arbitrarily) c) Design a four-bar mechanism by specifying the fixed pivot points (or moving pivot points)(erdman & Sandor) 7 4 U U 576 U crank-rocker path generating four-bar is required to advance film in a camera as shown (Erdman &Sandor). Given,, and φ, φ and selecting = i ; =-7.-.5i find the four-bar mechanism. = = i =-.+.5 i φ = φ = y x Es/es.5.

12 . Small autoclave is to be used to sterilize medical instruments. The door must be stored on the inside of the autoclave when it is open. The door must be closed by a mechanism from the inside to form a seal with a gasket that allows the steam pressure to reach 5 psi on the inside of the vessel, forcing the door to stay closed (as in the case of a steam cooker). Synthesize a four-bar mechanism for the autoclave door using the given three positions (If you cannot find a satisfactory solution using the given three positions, you can change the location of the mid position and its angle) (Erdman &Sandor). 4 (,) (86,85) (4,8) Es/es.5.

MENG 372 Chapter 3 Graphical Linkage Synthesis. All figures taken from Design of Machinery, 3 rd ed. Robert Norton 2003

MENG 372 Chapter 3 Graphical Linkage Synthesis All figures taken from Design of Machinery, 3 rd ed. Robert Norton 2003 1 Introduction Synthesis: to design or create a mechanism to give a certain motion