Four-Bar Linkage Mechanism Design

1. Ground Link (Link 1)

• Fixed base providing reference frame
• Contains pivot points for moving links

2. Input Link/Crank (Link 2)

• Driven link, may rotate fully or oscillate
• Determines mechanism configuration

3. Coupler (Link 3)

• Connects crank and follower
• Points on coupler trace complex curves

4. Output Link/Follower (Link 4)

• Produces desired motion output
• May rotate or oscillate depending on design

If the inequality holds (Grashof linkage):

• At least one link can rotate 360°
• Configuration depends on which link is ground

Which link is ground determines behavior:

• Crank-Rocker: Crank rotates 360°, follower oscillates
• Double-Crank (Drag-link): Both crank and follower rotate 360°
• Double-Rocker: Both crank and follower oscillate

If inequality doesn’t hold (Non-Grashof):

• No link can rotate fully; all oscillate

For this lesson, we’ll use:

Grashof Check:

In the spreadsheet, create this table:

Why Aliases?

Aliases let you reference cells by name instead of “B2”, making formulas readable and meaningful.

Create aliases:

1. Click cell B2

2. Right-click → Properties

3. In “Alias” field, type: Link1

4. Click OK

5. Repeat for all parameter cells (B2 through B8):

   • B2: Link1
   • B3: Link2
   • B4: Link3
   • B5: Link4
   • B6: LinkWidth
   • B7: LinkThickness
   • B8: PinRadius

Now you can use Spreadsheet.Link1 anywhere in your model!

Draw a horizontal line:

1. Line tool (press L)

2. Click at origin (0, 0)

3. Move horizontally to the right

4. Click to place endpoint

5. Press Escape

6. Make it horizontal:

   • Select the line
   • Press H key

7. Fix the start point:

   • Coincident constraint
   • Click left endpoint
   • Click origin

8. Dimension the link:

   • Distance constraint
   • Click both endpoints
   • Click ƒx button
   • Formula: Spreadsheet.Link1
   • Press Enter

Draw a line from point A:

1. Line tool (L)

2. Start at the left endpoint of Link 1 (point A)

3. Draw at an angle upward-right

4. Click to place endpoint

5. Press Escape

6. Constrain the link:

   • Coincident constraint
   • Click start of new line
   • Click left endpoint of Link 1 (point A)

7. Dimension the length:

   • Distance constraint
   • Click both endpoints of the new line
   • Click ƒx button
   • Formula: Spreadsheet.Link2
   • Press Enter

This is the crank, connecting joints A and C.

Draw a line from point B:

1. Line tool (L)

2. Start at right endpoint of Link 1 (point B)

3. Draw upward at an angle

4. Click to place endpoint

5. Press Escape

6. Constrain:

   • Coincident at point B
   • Distance = Spreadsheet.Link4

This is the follower, connecting joints B and D.

Draw a line connecting the free ends:

1. Line tool (L)

2. Start at free end of Link 2 (point C)

3. End at free end of Link 4 (point D)

4. Press Escape

5. Constrain:

   • Coincident at point C
   • Coincident at point D
   • Distance = Spreadsheet.Link3

Make sketch reference-only:

1. Select all four lines

   • Press Ctrl+A or box-select all lines

2. Toggle construction geometry

   • Press G key
   • Lines turn blue/dashed

Check and close:

1. Check constraints:

   The sketch should be fully constrained. Verify:

   • Link 1: horizontal, one end at origin, length ✓
   • Link 2: coincident at A, length ✓
   • Link 3: coincident at C and D, length ✓
   • Link 4: coincident at B, length ✓

2. Optional: Add angle dimension

   If under-constrained, add angle to Link 2:

   • Angle constraint
   • Link 2 to horizontal
   • Type: 30 degrees

3. Close the sketch

   Click Close button in toolbar

Reference master sketch geometry:

1. External geometry tool (press E)

2. Click the master sketch in the tree

3. Select joint A endpoint (origin)

4. Select joint B endpoint (right end of Link 1)

5. Press Escape

Draw circles at both joints:

1. Circle tool (C)

2. Draw circle centered at origin (joint A)

3. Press Escape

4. Circle tool again

5. Draw circle at joint B reference point

6. Press Escape

7. Constrain both circles:

   • Coincident: First circle center → origin reference
   • Coincident: Second circle center → joint B reference

8. Dimension the holes:

   • Radius constraint on first circle
   • Click ƒx → Spreadsheet.PinRadius
   • Repeat for second circle

Create the connecting plate:

1. Rectangle tool

2. Draw rectangle connecting the two circles

3. Press Escape

4. Symmetric constraint:

   • Select top edge of rectangle
   • Select bottom edge of rectangle
   • Select horizontal centerline between holes
   • This centers the rectangle on the link axis!

5. Dimension width:

   • Distance constraint (perpendicular to link)
   • Click ƒx → Spreadsheet.LinkWidth

Complete the sketch:

1. Verify fully constrained

   Check solver messages panel

2. Close sketch

   Click Close button

3. Pad the link

   • Select the sketch
   • Click Pad tool
   • Length: Click ƒx → Spreadsheet.LinkThickness
   • Click OK

1. Switch to Assembly workbench

   Use workbench dropdown

2. Create new assembly

   Assembly → Create Assembly

3. Add all four parts

   Drag from tree or use “Add Part” button:

   • Link1_Ground
   • Link2_Crank
   • Link3_Coupler
   • Link4_Follower

1. Select Link1_Ground in assembly tree

2. Click Fixed constraint button

3. Link 1 is now locked in place (ground reference)

Apply Axial Align constraints at all four joints:

1. Joint A (Link 1 - Link 2):

   • Select hole axis from Link 1 at point A
   • Select hole axis from Link 2 at point A
   • Click Axial Align constraint

2. Joint B (Link 1 - Link 4):

   • Link 1 hole at B
   • Link 4 hole at B
   • Axial Align

3. Joint C (Link 2 - Link 3):

   • Link 2 hole at C
   • Link 3 hole at C
   • Axial Align

4. Joint D (Link 3 - Link 4):

   • Link 3 hole at D
   • Link 4 hole at D
   • Axial Align

Test the mechanism:

1. Drag Link 2 (the crank) in the assembly view

2. Observe motion:

   • Link 2 should rotate smoothly through 360°
   • Link 3 follows with complex motion
   • Link 4 oscillates back and forth!

Troubleshooting:

1. Open Spreadsheet

   Double-click Spreadsheet in tree

2. Change Link2 to 50mm

   • Click cell B3
   • Type: 50
   • Press Enter

3. Recompute

   Press Ctrl+R or click Recompute button

4. Observe changes:

   • Crank is now longer!
   • Master sketch updates!
   • All four parts adapt!
   • Assembly maintains constraints!

✅ Success! Your mechanism is parametric!

Try these link length configurations:

Configuration 1: Crank-Rocker (original)

Link1 = 100, Link2 = 40, Link3 = 80, Link4 = 70

• Link2 rotates fully 360°
• Link4 oscillates

Configuration 2: Double-Rocker

Link1 = 40, Link2 = 100, Link3 = 80, Link4 = 70

• Now Link1 is shortest (but fixed)
• Both moving links oscillate!

Configuration 3: Non-Grashof

Link1 = 100, Link2 = 20, Link3 = 80, Link4 = 70

• Try even more extreme: Link1=100, Link2=10
• Mechanism may lock up!

Push the limits:

1. Set Link2 = 60, Link3 = 120

2. Recompute

3. Entire mechanism scales up!

Try different ratios:

• Long coupler: Link3 = 150
• Short follower: Link4 = 40
• Balanced: All links ≈ 80mm

Everything should update cleanly!

1. Add fillets

   Use Fillet tool to round sharp edges (2mm radius)

2. Add more parameters

   Control all dimensions via spreadsheet (currently some are hardcoded)

3. Create drawings for all four links

   Generate complete documentation set

1. Design connecting pins

   Create separate pin parts for each joint

2. Add a coupler point

   Place a marker on Link 3, observe its path

3. Create assembly drawing

   Show full mechanism with dimensions

1. Plot coupler curves

   Use Python to trace coupler point paths

2. Motion study

   Create animation showing one complete cycle

3. Design straight-line mechanism

   Find link ratios that create approximate straight-line motion (Chebyshev linkage)

4. Add velocity analysis

   Calculate and plot link angular velocities

“Parts don’t align in assembly”

“Mechanism is locked/won’t move”

“Master sketch is under-constrained”

“External geometry not updating”

“Parts don’t update with spreadsheet”