Graphical Synthesis: Motion Generation with Pivot...
Transcript of Graphical Synthesis: Motion Generation with Pivot...
At the end of this video, you should be able to:• Describe the concept of kinematic inversion• Graphically synthesize a four bar motion generator with three
precision positions by specifying the ground pivots
Graphical Synthesis: Motion Generation with Ground Pivot Specification
Kinematic Inversion: Considering the motion of a mechanism with different links as ground
Digression: Kinematic Inversion
3 Precision Position Motion Generation
A0
A0’
A0’’
1. Pick ground pivots (A0, B0)2. Find A0’ and A0’’ using
kinematic inversion– A0’ is the location of A0,
viewed from P2, drawn in 1stposition
3 Precision Position Motion Generation
A0
A0’
A0’’
A1
1. Pick ground pivots (A0, B0)2. Find A0’ and A0’’ using
kinematic inversion– A0’ is the location of A0,
viewed from P2, drawn in 1stposition
3. Find moving pivot A1 at center of A0, A0’, A0’’
3 Precision Position Motion Generation
A0
A0’
A0’’
A1
1. Pick ground pivots (A0, B0)2. Find A0’ and A0’’ using
kinematic inversion– A0’ is the location of A0,
viewed from P2, drawn in 1stposition
3. Find moving pivot A1 at center of A0, A0’, A0’’
4. Repeat for B side
3 Precision Position Motion Generation
A0
B0’
B0’’
A1
1. Pick ground pivots (A0, B0)2. Find A0’ and A0’’ using
kinematic inversion– A0’ is the location of A0,
viewed from P2, drawn in 1stposition
3. Find moving pivot A1 at center of A0, A0’, A0’’
4. Repeat for B side
B0
B1
3 Precision Position Motion Generation
A0
B0’
B0’’
A1
1. Pick ground pivots (A0, B0)2. Find A0’ and A0’’ using
kinematic inversion– A0’ is the location of A0,
viewed from P2, drawn in 1stposition
3. Find moving pivot A1 at center of A0, A0’, A0’’
4. Repeat for B side
B0
B1
3 Precision Position Motion Generation
A0
A1
1. Pick ground pivots (A0, B0)2. Find A0’ and A0’’ using
kinematic inversion– A0’ is the location of A0,
viewed from P2, drawn in 1stposition
3. Find moving pivot A1 at center of A0, A0’, A0’’
4. Repeat for B side
B0
B1
3 Precision Position Motion Generation
A0
B0’
B0’’
A1
1. Pick ground pivots (A0, B0)2. Find A0’ and A0’’ using
kinematic inversion– A0’ is the location of A0,
viewed from P2, drawn in 1stposition
3. Find moving pivot A1 at center of A0, A0’, A0’’
4. Repeat for B side
B0
B1
3 Precision Position Motion Generation
A0
A0’
A0’’
A1
1. Pick ground pivots (A0, B0)2. Find A0’ and A0’’ using
kinematic inversion– A0’ is the location of A0,
viewed from P2, drawn in 1stposition
3. Find moving pivot A1 at center of A0, A0’, A0’’
4. Repeat for B side
At the end of this video, you should be able to:• Graphically synthesize a path generation four bar mechanism
through three precision positions with and without specified timing
Graphical Synthesis: Path Generation
P1
P3
A2
A3
A0B0
A1
P2
B1
Path Generation
Source: Erdman, et al., Mechanism Design
Prescribed: P1, P2, P3
Graphical Path Synthesis
P1
P2
P3
A2
A3
Free Choices:1. A0 and B02. Input link length3. Initial input link angle
A0B0
A1α2
Procedure:1. Find A0’ and A0” by
grounding coupler
α3
Graphical Path Synthesis
P1
P2
P3
A2
A3
A0B0
A1α2
α3α2α3
A0’A0”
Prescribed: P1, P2, P3Free Choices:1. A0 and B02. Input link length3. Initial input link angle
Procedure:1. Find A0’ and A0” by
grounding coupler
Graphical Path Synthesis
P1
B0”P3
A2
A3
A0B0
A1
A0’A0”
P2
B0’
P3B0 from P1
P2B0 from P1
A0B0 from A0”
A0B0 from A0’
Prescribed: P1, P2, P3Free Choices:1. A0 and B02. Input link length3. Initial input link angle
Procedure:2. Locate B0’ and B0”
A0B0=A0’B0’=A0”B0” P2B0=P1B0’, P3B0=P1B0”
Graphical Path Synthesis
P1
P3
A2
A3
A0B0
A1
A0’A0”
P2
B0”
B0’
B1
Prescribed: P1, P2, P3Free Choices:1. A0 and B02. Input link length3. Initial input link angle
Procedure:3. Locate B1 with
perpendicular bisectors
Graphical Path Synthesis
P1
P3
A2
A3
A0B0
A1
P2
B1
Prescribed: P1, P2, P3Free Choices:1. A0 and B02. Input link length3. Initial input link angle
Procedure:4. Draw final mechanism
Graphical Path Synthesis: Free Choices
P1
P3
A2
A3
A0B0
A1
P2
B1
Prescribed: P1, P2, P3Free Choices:1. A0 and B02. Input link length3. Initial input link angle
• Timing: Specifying input link rotation between precision positions
Mechanism Timing
P1
P3
P2
LOW HIGH
MEDIUM
Prescribed Free Choices
Path Generation without Timing
Path Generation with Timing
Graphical Path Synthesis Free Choices
I. Find r2 and β1 using kinematic inversion grounding input link
II. Find B1 as done in Path w/o Timing synthesis
Path with Timing Synthesis Procedure
Graphical Path w/ Timing, Part I
P1
P3
P2’
P3’A0
P2
Prescribed: P1, P2, P3, β2=45°, β3=75°
Procedure:1. Pick A0
2. Draw A0P2 & A0P33. Invert (ground input link)
a) Locate P2’ by rotating P2A0 by –β2 about A0
b) Locate P3’ by rotating P3A0 by –β3 about A0
-β2
-β3
Graphical Path w/ Timing, Part I
P1
P3
P2’
P3’A0
P2
Prescribed: P1, P2, P3, β2=45°, β3=75°
Procedure:1. Pick A0
2. Draw A0P2 & A0P33. Invert (ground input link)
a) Locate P2’ by rotating P2A0 by –β2 about A0
b) Locate P3’ by rotating P3A0 by –β3 about A0
4. Find A1 at center of P1, P2’, P3’
A1
Graphical Path w/ Timing, Part I
P1
P3
P2’
P3’A0
P2
Prescribed: P1, P2, P3, β2=45°, β3=75°
Procedure:1. Pick A0
2. Draw A0P2 & A0P33. Invert (ground input link)
a) Locate P2’ by rotating P2A0 by –β2 about A0
b) Locate P3’ by rotating P3A0 by –β3 about A0
4. Find A1 at center of P1, P2’, P3’
5. Repeat Path w/o Timing Synthesis
-β2
-β3
A1
Graphical Path w/ Timing, Part I
P1
P3
A0
P2
Prescribed: P1, P2, P3, β2=45°, β3=75°
Procedure:1. Pick A0
2. Draw A0P2 & A0P33. Invert (ground input link)
a) Locate P2’ by rotating P2A0 by –β2 about A0
b) Locate P3’ by rotating P3A0 by –β3 about A0
4. Find A1 at center of P1, P2’, P3’
5. Repeat Path w/o Timing Synthesis
A1
A2
A3