Chapter 2 Graphical Synthesis of Mechanisms

Transcription

1 esign and Production Engineering epartment hapter 2 Graphical Synthesis of Mechanisms MT 251 s s t. P r o f. Mohammed M. Hedaya 2.1. Types of Synthesis of Mechanisms Function generation The correlation of an input motion with an output motion. θ = f β Mechanical analog computers Mechanical function generators applications rtillery rangefinders and shipboard gun aiming system Path generation The control of a point in the plane such that it follows some prescribed path. 2 1

2 2.1. Types of Synthesis Motion generation The control of a line in the plane such that it passes some prescribed set of sequential positions. rientation of the link containing the line is important. The course scope Motion Two Position Synthesis 3 Theory of machines and multibody (MT251 ) hapter 2: Graphical Linkage Synthesis 2.2. Extreme positions 4 bar mechanism 4 Theory of machines and multibody (MT251 ) hapter 2: Graphical Linkage Synthesis 2

3 2.2. Extreme positions (cont.) From pen the compass with length + From pen the compass with length arc of (+) arc of () Extreme positions (cont.) From pen the compass with length - From pen the compass with length arc of (-) arc of () 6 3

4 2.2. Extreme positions (cont.) From 1 to 2 : β From 2 to 1 : φ δ = β 180 =, δ = 180 φ 2 1 δ = 180 φ 2δ = β φ β δ 1 θ 2 φ Synthesis of four-bar mechanism Rocker-output Equal time for go and return ngular displacements omplex motion uick return oupler-output 8 4

5 Rocker-output, equal time for go and return ngular displacement θ Rocker-output, equal time for go and return (cont.) ngular displacement Ground: rank: oupler: utput : θ 10 5

6 Rocker-output, equal time for go and return (cont.) ngular displacement Given ngle Steps 1. raw the output link in both extreme positions, in any convenient location. 2. raw the chord 1 2 and extend it in any convenient direction. 3. Select a convenient point on line 1 2 extended. 4. isect line segment 1 2, and draw a circle of that radius about. 5. Label the two intersections of the circle and 1 2 extended, 1 and Measure the length of the coupler as 1 to 1 or 2 to Measure ground length, crank length, and rocker length Rocker-output, equal time for go and return (cont.)

7 Rocker-output, equal time for go and return (cont.) Ground:, specific position of rank: oupler: utput : (specific shape) Rocker-output, equal time for go and return (cont.) Given Two positions of a line Steps 1. raw line from point 1 to 2 and bisect it. 2. raw line from point 1 to 2 and bisect it. 3. Set the intersection of the bisectors as a grounded pair of the rocker. 4. onstruct the rocker. 5. raw arc of a suitable radius to determine a connection point. 6. raw the output link in both extreme positions, in any convenient location. 14 7

8 Rocker-output, equal time for go and return (cont.) Given Two positions of a line Steps (cont.) 7. raw the chord 1 2 and extend it in any convenient direction. 8. Select a convenient point on line 1 2 extended. 9. isect line segment 1 2, and draw a circle of that radius about. 10. Label the two intersections of the circle and 1 2 extended, 1 and Measure the length of the coupler as 1 to 1 or 2 to Measure ground length, crank length, and rocker length Rocker-output, quick return ngular displacement 1 2 δ 1 θ

9 Rocker-output, quick return (cont.) ngular displacement Ground:, specific position of rank: oupler: utput : θ Rocker-output, quick return (cont.) ngular displacement Given ngle Steps 1. raw the output link in both extreme positions, in any convenient location. 2. onstruct a line through a point 1 in any convenient angle. 3. onstruct a line through a point 2 at angle δ with the previous line. 4. Label the intersection of the two lines. 5. raw a circle with centre and radius equal crank length = ( 1 2 )/2. 6. Label the intersections of the circle and 1 and with 2 extension as 1 and Measure the length of the coupler as 1 to 1 or 2 to Measure ground length and rocker length. 18 9

10 oupler-output oupler-output (cont.) 1 Ground: Rockers:, oupler/ utput:

11 oupler-output (cont.) Given Two positions of a line Steps 1. raw line from point 1 to 2 and bisect it. 2. raw line from point 1 to 2 and bisect it. 3. Select suitable positions for grounded pairs and. 4. Measure the length of the rockers and 5. Measure ground length. 6. heck that the mechanism is double-lever. If not repeat steps from step Solved examples esign a four-bar mechanism to produce 30 rocking angle of the output

12 2.4. Solved examples esign a four-bar mechanism to produce 30 rocking angle of the output, where the ratio between forward and return times is 1.5: Solved examples esign a four-bar mechanism to transfer the shown box between the shown positions, where the ratio between forward and return times is 1.5:

13 2.4. Solved examples esign a four-bar mechanism to transfer the shown box between the shown positions. Use the coupler as an output link