Scotch Yoke Mechanism

1. Rotating Crank

• Circular disk with eccentric pin
• Pin offset determines stroke

2. Yoke (Slider)

• Block with horizontal slot
• Constrained to linear motion

3. Pin-in-Slot Connection

• Pin slides within yoke slot as crank rotates
• Continuous sliding contact

4. Guide Rails

• Constrain yoke to linear motion only
• Prevent rotation

Perfect Sinusoidal Relationship:

Where:

• = crank radius (eccentricity)
• = angular velocity
• = time

Key Characteristic: Yoke displacement is exactly proportional to sin(θ), where θ is crank angle.

When to Choose Scotch Yoke:

• Pure sinusoidal motion required
• Compact design needed
• Lower speeds acceptable
• Simple construction preferred

When to Choose Slider-Crank:

• High-speed operation
• Minimize wear
• Standard parts available

Part Design

• Creating individual parametric parts
• Primary workbench for crank, yoke, guides

Sketcher

• 2D profiles for slots, circles, rectangles
• Constraint-based geometry

Spreadsheet

• Parameter control center
• Formulas for calculated values

Assembly

• Combining parts with motion constraints
• Testing mechanism movement

TechDraw

• Engineering drawings
• Documentation with dimensions

Enter header row:

Enter primary parameters:

Add calculated parameters using formulas:

In cell B4, enter formula: =B2*2

Add yoke and crank geometry:

Critical Step: Create aliases for all parameter values!

For each parameter in column B:

1. Click cell B2 (CrankRadius value)

2. Right-click → Properties

3. In “Alias” field, type: CrankRadius

4. Click OK

5. Repeat for all B column parameter cells:

   • B3 → PinDiameter
   • B4 → Stroke
   • B5 → PinRadius
   • B6 → SlotWidth
   • B7 → SlotLength
   • B8 → YokeWidth
   • B9 → YokeHeight
   • B10 → YokeThickness
   • B11 → CrankDiskRadius
   • B12 → CrankThickness
   • B13 → ShaftDiameter
   • B14 → ShaftRadius
   • B15 → GuideLength

Now you can reference Spreadsheet.CrankRadius throughout your model!

1. Draw the outer circle

   • Click Circle tool (or press C)
   • Click at the origin (white/yellow dot at center)
   • Move mouse outward and click to complete
   • Press Escape

2. Add parametric radius constraint

   • Click Radius constraint tool
   • Click the circle
   • In the dimension dialog, click ƒx button
   • Type: Spreadsheet.CrankDiskRadius
   • Press Enter

   Circle now shows 60mm and will update with parameters!

1. Draw shaft hole circle

   • Circle tool (C)
   • Click at origin
   • Draw smaller circle inside
   • Press Escape

2. Make concentric with origin

   • Click Coincident constraint tool
   • Click the center of this circle
   • Click the origin point
   • Press Escape

   Circle is now locked to center

3. Add parametric radius

   • Radius constraint tool
   • Click the shaft hole circle
   • Click ƒx button
   • Type: Spreadsheet.ShaftRadius
   • Press Enter

   10mm radius shaft hole created (half of 20mm diameter)

1. Draw pin circle

   • Circle tool (C)
   • Click to the right of center (approximate)
   • Draw a small circle
   • Press Escape

2. Make horizontally aligned with origin

   • Click Horizontal constraint tool
   • Click the center of the pin circle
   • Click the origin
   • Press Escape

   Pin is now on horizontal centerline

3. Set distance from origin (CRITICAL!)

   • Click Distance constraint tool
   • Click the origin point
   • Click the center of the pin circle
   • Click ƒx button
   • Type: Spreadsheet.CrankRadius
   • Press Enter

   Pin is now 40mm from center. This IS the crank radius!

4. Set pin radius

   • Radius constraint tool
   • Click the pin circle
   • Click ƒx button
   • Type: Spreadsheet.PinRadius
   • Press Enter

   6mm radius pin (half of 12mm diameter)

1. Check solver

   Look at “Solver Messages” panel:

   • Should say “Fully constrained”

2. Close the sketch

   Click Close button

3. Pad the crank disk

   • Select the sketch in tree
   • Click Pad tool
   • Length: Click ƒx → Spreadsheet.CrankThickness
   • Click OK

   3D crank disk created!

1. Create new sketch

   • Select Crank body in tree
   • Click Create Sketch
   • Select the flat face of the crank disk (the top surface)
   • Click OK

2. Draw pin circle

   • Circle tool (C)
   • Click at the position where the eccentric pin hole is
   • The sketch should snap to the existing pin center
   • Press Escape

3. Constrain to existing geometry

   • The circle center should automatically be coincident with the pin hole center
   • If not, add Coincident constraint manually

4. Set radius

   • Radius constraint
   • Click the circle
   • Click ƒx → Spreadsheet.PinRadius
   • Enter

5. Close sketch

6. Pad the pin

   • Select the new sketch
   • Click Pad
   • Length: 25 mm (enough to engage yoke slot)
   • Click OK

   Protruding pin created!

1. Draw outer rectangle

   • Click Rectangle tool
   • Draw rectangle centered approximately at origin
   • Press Escape

2. Center about origin

   You need the rectangle symmetric about both axes.

   Method 1: Symmetric constraints

   • Select left edge of rectangle
   • Select right edge of rectangle
   • Select Y-axis (vertical line through origin)
   • Click Symmetric constraint
   • Repeat for top/bottom edges about X-axis

   Method 2: Constrain center point

   • Click Coincident constraint
   • Click rectangle center point
   • Click origin

3. Dimension width (horizontal)

   • Distance constraint
   • Click left edge
   • Click right edge
   • Click ƒx → Spreadsheet.YokeWidth
   • Enter (60mm)

4. Dimension height (vertical)

   • Distance constraint
   • Click top edge
   • Click bottom edge
   • Click ƒx → Spreadsheet.YokeHeight
   • Enter (80mm)

Outer yoke body is now defined and centered!

1. Draw slot rectangle

   • Rectangle tool
   • Draw horizontal rectangle in center of yoke
   • Press Escape

2. Center slot on yoke

   • Symmetric constraint
   • Select slot left edge, slot right edge, Y-axis
   • Symmetric constraint
   • Select slot top edge, slot bottom edge, X-axis

   Slot is now centered both horizontally and vertically

3. Dimension slot length (horizontal direction)

   • Distance constraint
   • Click slot left edge
   • Click slot right edge
   • Click ƒx → Spreadsheet.SlotLength
   • Enter (110mm = Stroke + 30mm margin)

4. Dimension slot width (vertical direction)

   • Distance constraint
   • Click slot top edge
   • Click slot bottom edge
   • Click ƒx → Spreadsheet.SlotWidth
   • Enter (14mm = PinDiameter + 2mm clearance)

For smoother pin travel, you can round the slot ends:

1. Add circles at slot ends

   • Circle tool
   • Draw circle at left end of slot
   • Radius = SlotWidth / 2 = 7mm
   • Coincident with slot left edge midpoint
   • Tangent to slot top and bottom edges

2. Repeat for right end

   • Circle at right end
   • Same constraints

This creates rounded “racetrack” slot shape for reduced wear.

For simplicity in this lesson, you can skip this step and use rectangular slot.

1. Verify fully constrained

   Solver should show: “Fully constrained”

2. Close the sketch

   Click Close button

3. Pad the yoke

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

   3D yoke with slot created!

View the yoke in 3D (rotate view) - you should see a block with a horizontal slot through it!

1. Create Body

   • Create Body → Rename to GuideRail_Left

2. Create Sketch on XZ_Plane (vertical plane)

   This plane is perpendicular to the yoke’s direction of travel

3. Draw rail profile

   • Rectangle tool
   • Width: 15mm (rail width)
   • Height: 25mm (rail height)
   • Position to left side, appropriate to yoke edge

4. Position the rail

   You want it positioned so the yoke will slide against it.

   Typical approach:

   • Distance from center: About YokeWidth/2 + small gap
   • Or position against yoke side surface

5. Close sketch

6. Pad along Y-axis

   • Click Pad
   • Type: Dimension
   • Length: Click ƒx → Spreadsheet.GuideLength
   • Direction: Ensure it extrudes along Y (yoke travel direction)
   • Click OK

   Left guide rail created spanning 200mm!

You can either:

Option A: Mirror the left rail (if FreeCAD supports it in your workflow)

Option B: Create manually (recommended for learning):

1. Create Body

   • Create Body → Rename to GuideRail_Right

2. Create Sketch on XZ_Plane

3. Draw rail profile

   • Rectangle: 15mm × 25mm
   • Position to right side (mirror position of left rail)

4. Close sketch

5. Pad

   • Length: Click ƒx → Spreadsheet.GuideLength
   • Click OK

Both guide rails complete!

Alternative approach: Sketch rails on the same plane as simple rectangles at appropriate X-positions, then pad both in same body. This ensures perfect parallelism.

1. Switch to Assembly workbench

   Use workbench dropdown

   Assembly 4 or A2plus

   (Instructions assume Assembly workbench availability)

2. Create new assembly

   Assembly → Create Assembly

3. Add parts

   Drag from tree or use “Add Part” button:

   • Frame
   • Crank
   • Yoke
   • GuideRail_Left
   • GuideRail_Right

1. Fix the frame

   • Select Frame in assembly tree
   • Click Fixed constraint button
   • Frame is now locked in place

2. Allow crank rotation

   • Select crank shaft hole axis
   • Select frame shaft hole axis
   • Click Axial Align constraint

   This aligns the axes and allows rotation!

3. Test crank rotation

   Try dragging the crank in the assembly view - it should rotate about the shaft axis

1. Position yoke initially

   Move yoke so it’s between the guide rails and the crank pin is within the slot

2. Constrain yoke to guides

   Option A: Plane constraints

   • Select yoke bottom face
   • Select frame top face
   • Apply Plane coincident constraint

   Option B: Linear motion constraint

   • If your assembly workbench supports it
   • Define linear motion along Y-axis only

3. Add guide rail constraints

   • Constrain yoke side faces to guide rail inner faces
   • Allow sliding along Y-axis
   • Prevent rotation and X-axis movement

The yoke should now only be able to move horizontally (along Y-axis)!

For verification:

Position the crank at different angles (0°, 90°, 180°, 270°) and manually position the yoke to match. The pin should always be within the slot bounds!

Manually verify these positions:

1. Rotate crank to 0° (pin pointing right)
2. Position yoke at maximum right position
3. Verify pin is in slot
4. Repeat for other angles

Verify stroke = 2 × CrankRadius:

1. Measure yoke position at maximum right (crank at 0°)

   Should be: x = +CrankRadius = +40mm

2. Measure yoke position at maximum left (crank at 180°)

   Should be: x = -CrankRadius = -40mm

3. Calculate stroke

   Stroke = 40 - (-40) = 80mm = 2 × 40mm ✓

Add these key dimensions:

• Stroke: 80mm (yoke travel distance)
• Crank radius: 40mm (pin offset from shaft center)
• Slot width: 14mm (pin diameter + clearance)
• Slot length: 110mm (stroke + margin)
• Clearance: 2mm (slot width - pin diameter)

Use TechDraw dimension tools: Horizontal, Vertical, Radius

Create a diagram showing sinusoidal displacement:

In a separate area of the drawing:

1. Draw crank at 4 positions: 0°, 90°, 180°, 270°
2. Show corresponding yoke positions
3. Plot curve: x = r × sin(θ)

Table of values:

Add text annotations:

Title block:

• Part: Scotch Yoke Assembly
• Scale: 1:2 (or appropriate)
• Material: Steel (or as designed)
• Designer: Your name
• Date: 2025-12-17

1. Review drawing

   Verify all dimensions and views are clear

2. Export as PDF

   • Right-click page → Export as PDF
   • Save as ScotchYoke_Assembly.pdf

3. Optional: Export as DXF

   For CAM or further processing

Professional engineering documentation complete!

1. Open Spreadsheet

   Double-click Spreadsheet in tree

2. Change CrankRadius

   • Click cell B2
   • Type: 50
   • Press Enter

3. Observe automatic updates

   Check these cells update automatically:

   • B4 (Stroke): Should now be 100mm (2 × 50)
   • B7 (SlotLength): Should now be 130mm (100 + 30)
   • B11 (CrankDiskRadius): Should now be 70mm (50 + 20)

4. Recompute

   Press Ctrl+R or click Recompute button

5. Verify geometric changes

   • Crank pin moves outward to 50mm from center
   • Yoke slot lengthens to 130mm
   • Crank disk grows to 70mm radius
   • Assembly updates!

✅ Success! Stroke increased from 80mm to 100mm automatically!

1. Change PinDiameter

   • Cell B3: Type 16 (was 12mm)
   • Enter

2. Check automatic updates

   • B5 (PinRadius): Now 8mm (16/2)
   • B6 (SlotWidth): Now 18mm (16 + 2)

3. Recompute (Ctrl+R)

4. Verify:

   • Crank pin grows to 8mm radius
   • Yoke slot width increases to 18mm
   • 2mm clearance maintained!

✅ Clearance automatically preserved!

Test robustness with extreme parameters:

1. Small mechanism

   • CrankRadius = 20mm
   • PinDiameter = 8mm
   • Recompute

   Everything scales down correctly!

2. Large mechanism

   • CrankRadius = 80mm
   • PinDiameter = 20mm
   • Recompute

   Everything scales up!

3. Return to design values

   • CrankRadius = 40mm
   • PinDiameter = 12mm
   • Recompute

All relationships maintain correctly across the range!

Verify clearances are maintained:

1. Check slot width formula

   Cell B6 should show: =B3+2

2. Test clearance change

   • Edit formula to: =B3+3 (3mm clearance)
   • SlotWidth updates to 15mm
   • Recompute
   • Slot is now looser!

3. Restore original

   • Back to =B3+2

Critical insight: By using formulas for clearances, you can instantly explore tighter or looser fits without manual recalculation!

Position of yoke as function of crank angle:

Where:

• = yoke position from center (mm)
• = crank radius (40mm)
• = crank angle (radians or degrees)

Example calculations:

Velocity of yoke (derivative of displacement):

Where:

• = angular velocity of crank (rad/s)

At constant crank speed rad/s (about 19 RPM):

Key insight: Velocity is maximum at center position () and zero at extremes ()!

Acceleration of yoke (derivative of velocity):

Where:

• = angular velocity (rad/s)

At rad/s:

Critical observation:

Acceleration is proportional and opposite to displacement. This is the defining characteristic of simple harmonic motion!

This is the same physics as:

• Mass on a spring
• Pendulum (small angles)
• Wave motion

Sliding friction in slot:

Where:

• = coefficient of friction (slot/pin interface)
• = normal force from pin on slot sides

Normal force depends on:

• Crank torque
• Acceleration forces
• External load on yoke

To reduce friction:

• Use low-friction materials (bronze bushing in slot)
• Lubrication (oil grooves in slot)
• Roller bearings at slot contact points (advanced)

Why Scotch yoke has higher friction than slider-crank:

• Continuous sliding contact vs. pivoting joints
• Sliding velocity = (not zero)

1. Add fillets to yoke

   Round sharp corners for reduced stress concentration (3mm radius)

2. Create lubrication grooves

   Add channels in slot for oil distribution

3. Add more parameters

   Control guide rail dimensions, frame size via spreadsheet

4. Design bearing mounts

   Add detailed shaft bearing geometry in frame

1. Create adjustable crank radius mechanism

   Design sliding pin mount on crank for variable stroke

2. Add counterweights

   Balance the rotating crank for smoother operation

3. Design double Scotch yoke

   Two opposing yokes on same crank for balanced forces

4. Create exploded view

   Show assembly sequence in TechDraw

1. Add roller bearings in slot

   Replace sliding contact with rolling elements

2. FEM stress analysis

   Use FreeCAD FEM workbench to analyze yoke stresses at extreme positions

3. Motion simulation

   Use animation tools to visualize sinusoidal motion

4. Calculate required motor torque

   Based on load, friction, acceleration

5. Design complete actuator

   Add motor, gearbox, limit switches, housing

“Pin binds in slot”

“Slot not centered on yoke”

“Stroke doesn’t update when CrankRadius changes”

“Clearance not maintained when pin size changes”

“Yoke rotates instead of sliding linearly”

“Pin doesn’t stay in slot during rotation”

“Measured stroke doesn’t equal 2 × CrankRadius”

“Yoke travel exceeds slot length”

Typical applications:

• Control valve actuators
• Material testing (sinusoidal loading)
• Educational demonstrations
• Reciprocating pumps (oil-free)

Typical applications:

• Internal combustion engines
• Compressors (high-speed)
• Industrial machinery
• Automotive systems