Cams and Cam-Follower Design: Engineering Motion from First Principles

Engineering Motion from First Principles

What Exactly Is a Cam — And Why Should You Care?

Before the practitioner could fix anything, the practitioner made him answer a deceptively simple question:

"What does a cam actually do?"

A cam is a mechanical component — usually a rotating or sliding piece with a specially shaped profile — that converts one type of motion into another. Specifically, it transforms rotary motion (a spinning shaft) into precise, predetermined linear or oscillating motion (a follower moving up, down, or swinging through an arc).

Think of it this way: a gear converts rotation into rotation. A cam converts rotation into programmed movement.

That "program" is literally carved into the shape of the cam. Every curve, every rise, every dwell is a physical instruction that tells the follower exactly where to be at every fraction of a revolution.

Where You'll Find Cams

Cams are everywhere in engineered systems:

• Internal combustion engines — opening and closing valves with split-second precision
• Automated manufacturing — indexing, feeding, cutting, and assembling parts at high speed
• Textile machinery — controlling thread tension and fabric feed
• Printing presses — timing ink rollers and paper feed
• Packaging equipment — folding, sealing, and labeling at hundreds of cycles per minute
• Musical instruments — player pianos and mechanical organs
• Locks and security mechanisms — translating key rotation into bolt movement

The Fundamental Promise of Cam Design

Unlike linkages or gears, a cam allows you to design any motion profile you want. Need the follower to accelerate gently, coast at constant speed, decelerate smoothly, then sit still for half a revolution? You can design a cam that does exactly that.

But here's the trap — and the reason the practitioner's machine was failing:

The shape of the cam determines not just where the follower goes, but how it gets there. And "how" determines whether the machine runs quietly for decades or destroys itself in hours.

Classes of Cams: The Two Fundamental Families

the practitioner started the practitioner's education with the broadest classification.

Cams can be divided into two primary classes:

. Uniform Motion Cams

A uniform motion cam moves the follower at the same rate of speed from the beginning to the end of the stroke. The displacement diagram is a straight line — elegant in its simplicity.

The problem? The movement starts from zero speed and jumps to full speed instantaneously. It also stops the same way — full speed to zero in an instant. At any meaningful operating speed, this produces a distinct, violent shock at the beginning and end of every stroke.

This was exactly the practitioner's problem. The previous engineer had designed a constant-velocity cam for a machine running at 900 RPM. At that speed, the "instantaneous" velocity changes produced theoretically infinite accelerations at the transition points. No follower system can survive that.

. Accelerated Motion Cams

Accelerated motion cams address the shock problem by controlling how the follower speeds up and slows down. Instead of snapping from rest to full speed, the follower is eased into motion along a mathematically defined curve.

Within this family, several specific motion curves exist, each with distinct characteristics:

the practitioner pointed at the table. "Notice that cycloidal motion has the highest calculated maximum acceleration. You'd think that makes it the worst choice. But read the fine print."

The fine print would change everything the practitioner understood about cam design.

Cam Follower Systems: The Three Workhorses

Before diving into displacement curves, you need to understand how the cam actually interfaces with the mechanism it drives. The three most commonly used cam-and-follower systems are:

A. Radial Translating Roller Follower

The roller follower sits directly above (or below) the cam's center of rotation. As the cam rotates, the roller translates — moves straight up and straight down — along a line that passes through the cam shaft center.

Characteristics:

• Simplest geometry
• Easy to analyze
• Pressure angle changes throughout the cycle
• Best for straightforward rise-dwell-return applications

B. Offset Translating Roller Follower

Identical to the radial follower, except the line of follower motion is offset from the cam center by a distance e. This offset shifts the geometry of the cam-follower interaction.

Why offset?

• Reduces the maximum pressure angle during the rise portion of the cam cycle
• Allows a smaller cam for the same motion requirements
• Introduces asymmetry that can be exploited to optimize rise vs. return characteristics

C. Swinging Roller Follower

Instead of translating in a straight line, the follower swings through an arc, pivoting around a fixed point M. The roller rides on the cam surface and the swinging arm transmits motion to the mechanism.

Characteristics:

• Compact packaging
• Natural for applications requiring angular output
• Higher allowable pressure angles (up to 45° vs. 30° for translating followers)
• More complex profile determination

Open-Track vs. Closed-Track Cams

Each of the above systems can be implemented as either:

• Open-track: The roller rides on one surface of the cam. A spring keeps the roller in contact during the return stroke. These build smaller but require reliable spring force at all speeds.

• Closed-track (grooved or conjugate): The roller rides in a groove or between two conjugate cam surfaces. This provides positive drive in both directions — no spring needed. Critical in applications where a broken spring could cause catastrophic machine damage.

The trade-off is clear:

Displacement Diagrams: Where Every Cam Begins

the practitioner pulled out a fresh sheet of graph paper.

"Every cam design begins here," she said. "Not with the shape of the cam. With the story of how the follower moves."

A displacement diagram is a graph that plots follower position (vertical axis) against cam rotation (horizontal axis). One complete revolution of the cam — 360° — represents one complete cycle.

Anatomy of a Displacement Diagram

Consider a simple cam that must:

1. Rise the follower a distance h over 100° of cam rotation
2. Dwell (hold the follower still) for 20°
3. Return the follower to its starting position over 180°
4. Dwell again for 60°

The horizontal axis is divided into these four segments: T₁ (rise), T₂ (dwell), T₃ (return), T₄ (dwell). The vertical axis shows the follower displacement from 0 to h.

Displacement (y)
    h |         __
      |        /           \
      |       /             \
      |      /               \
      |     /                 \
      |    /                   \
      |   /                     \
    0 |__/                       \__
      |---|---------|-------------|-----------|
      0  100°     120°          300°        360°
         Rise     Dwell         Return      Dwell

The critical insight: The shape of the rise and return curves on this diagram — whether they're straight lines, parabolas, sine waves, or cycloids — completely determines the velocity, acceleration, and dynamic behavior of the follower.

Why the Shape of the Curve Matters More Than You Think

The displacement diagram is not just a picture. It is the source code of the cam.

• The first derivative of displacement with respect to time gives velocity
• The second derivative gives acceleration
• The third derivative gives jerk — the rate of change of acceleration

And here's the engineering reality: forces are proportional to acceleration (F = ma). So the acceleration curve directly tells you the forces the cam and follower must endure.

A cam with smooth acceleration produces gentle forces. A cam with sudden acceleration changes produces violent shocks. A cam with theoretically infinite acceleration at any point will, at high speed, destroy itself.

The Four Displacement Curves That Matter Most

the practitioner laid out four displacement diagrams, each with its associated velocity and acceleration curves. "Master these four, and you can design any cam the world will ever need."

Key Symbols and Relationships

Before examining each curve, here are the essential variables:

Fundamental relationships:

$$v = \frac{dy}{dt} = \omega \frac{dy}{d\phi}$$

$$a = \frac{d^2y}{dt^2} = \omega^2 \frac{d^2y}{d\phi^2}$$

Curve 1: Constant Velocity Motion

The Equation:

$$y = h \cdot \frac{t}{T} = h \cdot \frac{\phi}{\beta}$$

$$v = \frac{h}{T} = \frac{h\omega}{\beta}$$

$$a = 0 \quad \text{(except at } t = 0 \text{ and } t = T \text{ where } a \to \infty\text{)}$$

What It Looks Like:

The displacement diagram is a straight line. Velocity is constant. Acceleration is zero throughout — except at the very beginning and very end of the stroke, where it is theoretically infinite.

The Verdict:

In its raw, unmodified form, constant velocity motion is rarely used except in crude, low-speed devices. However, the advantage of uniform velocity is so valuable that by modifying the start and finish (blending in parabolic or cycloidal curves), this motion can be made practical. This technique is called Displacement Diagram Synthesis and is covered in detail later.

Curve 2: Parabolic Motion (Constant Acceleration)

The Equations:

First half of stroke (0 ≤ t ≤ T/2, acceleration phase):

$$y = 2h\left(\frac{t}{T}\right)^2 = 2h\left(\frac{\phi}{\beta}\right)^2$$

$$v = \frac{4ht}{T^2} = \frac{4h\omega\phi}{\beta^2}$$

$$a = \frac{4h}{T^2} = 4h\left(\frac{\omega}{\beta}\right)^2$$

Second half of stroke (T/2 ≤ t ≤ T, deceleration phase):

$$y = h\left[1 - 2\left(1 - \frac{t}{T}\right)^2\right] = h\left[1 - 2\left(1 - \frac{\phi}{\beta}\right)^2\right]$$

$$v = \frac{4h}{T}\left(1 - \frac{t}{T}\right) = \frac{4h\omega}{\beta}\left(1 - \frac{\phi}{\beta}\right)$$

$$a = -\frac{4h}{T^2} = -4h\left(\frac{\omega}{\beta}\right)^2$$

What It Looks Like:

The displacement curve is two parabolic segments joined at the midpoint. The velocity rises linearly from zero, peaks at mid-stroke, then falls linearly back to zero. The acceleration is a constant positive value in the first half and a constant negative value (deceleration) in the second half.

The Great Advantage:

For a given cam rotation angle and rise, parabolic motion produces the smallest possible maximum acceleration. This means the lowest possible inertia forces — on paper.

The Hidden Danger:

The acceleration curve has sudden, discontinuous changes at three critical points:

1. Beginning of stroke — acceleration jumps from 0 to +4h/T²
2. Middle of stroke — acceleration jumps from +4h/T² to −4h/T²
3. End of stroke — acceleration jumps from −4h/T² to 0

These instantaneous changes in acceleration are called jerk (or pulse). In a perfectly rigid system with zero backlash, this wouldn't matter. But no real mechanical system is perfectly rigid. Every real follower train has elasticity, backlash, and compliance.

The result: At high speeds, the actual dynamic forces acting on a parabolic cam are doubled and sometimes even tripled compared to the theoretical values. The calculated acceleration forces must be multiplied by a factor of at least 2 to account for load-increasing effects of elasticity and backlash.

Curve 3: Simple Harmonic Motion

The Equations:

$$y = \frac{h}{2}\left(1 - \cos\frac{180°t}{T}\right) = \frac{h}{2}\left(1 - \cos\frac{180°\phi}{\beta}\right)$$

$$v = \frac{h}{2} \cdot \frac{\pi}{T} \cdot \sin\frac{180°t}{T} = \frac{h}{2} \cdot \frac{\pi\omega}{\beta} \cdot \sin\frac{180°\phi}{\beta}$$

$$a = \frac{h}{2} \cdot \frac{\pi^2}{T^2} \cdot \cos\frac{180°t}{T} = \frac{h}{2} \cdot \left(\frac{\pi\omega}{\beta}\right)^2 \cdot \cos\frac{180°\phi}{\beta}$$

What It Looks Like:

The displacement follows a cosine-based curve. Velocity is smooth and sinusoidal during the stroke. Acceleration is also sinusoidal — smooth during the stroke but with instantaneous changes at the beginning and end.

Strengths:

Velocity and acceleration are smooth and continuous during the stroke. No sudden mid-stroke transitions like parabolic motion.

Weakness:

The instantaneous acceleration changes at the endpoints tend to cause vibration, noise, and wear. The maximum acceleration values occur at the ends of the stroke where the follower is starting or stopping — exactly where inertia loads must be overcome. The resulting forces can be much larger than externally applied loads.

Curve 4: Cycloidal Motion — The Champion of High-Speed Design

The Equations:

$$y = h\left(\frac{\phi}{\beta} - \frac{1}{2\pi}\sin\frac{360°\phi}{\beta}\right)$$

$$v = \frac{h\omega}{\beta} \cdot \frac{180°}{\pi} \cdot \left(1 - \cos\frac{360°\phi}{\beta}\right)$$

$$a = \frac{2\pi h\omega^2}{\beta^2} \cdot \sin\frac{360°\phi}{\beta}$$

What It Looks Like:

The displacement curve can be generated from a cycloid — the path traced by a point on the circumference of a circle rolling along a straight line. The velocity curve is smooth, starting and ending at zero. And the acceleration curve is a complete sine wave — smooth, continuous, and with absolutely no abrupt changes anywhere.

Why Cycloidal Motion Wins at High Speed:

Here's the paradox that the practitioner made the practitioner wrestle with:

The calculated maximum acceleration of a cycloidal cam is higher than that of a parabolic cam. By pure mathematics, parabolic looks better.

But in reality, at high speeds, the cycloidal cam produces dramatically lower actual forces.

The reason is jerk. Parabolic motion has sudden, discontinuous jumps in acceleration. Each jump sends a shockwave through the follower train, amplified by every bit of elasticity, backlash, and flexibility in the system. The actual forces are 2× to 3× the calculated values.

Cycloidal motion has gradually changing acceleration — the jerk is finite and smooth everywhere. The actual dynamic forces are only slightly higher than the theoretical values. The correction factor is just 1.05 for cycloidal motion, compared to at least 2.0 for parabolic.

The bottom line for design practice:

Cycloidal motion is the standard choice for high-speed cam design because it results in low levels of noise, vibration, and wear — despite having the highest theoretical acceleration.

Displacement Diagram Synthesis: Building Better Motion From Components

the practitioner now understood why his machine was failing. But the practitioner wasn't done. She showed him a technique that unlocks the full potential of cam design.

"What if you could take the best feature of constant velocity — uniform speed — and combine it with a smooth start and stop?"

This is Displacement Diagram Synthesis — the art of matching different cam curves together to create composite displacement diagrams.

Matching Parabolic Curves to Constant Velocity

The principle is elegant: take a straight-line (constant velocity) displacement diagram and replace the abrupt start and stop with parabolic curves.

A parabolic curve has a key geometric property: if you draw a parabola with its vertex at point O and a tangent at point P, that tangent intersects the baseline at the midpoint of the horizontal distance. This means the tangent at the junction point automatically represents the velocity of the follower — which equals the constant velocity of the straight-line section.

The result: The follower begins its stroke at zero velocity, accelerates smoothly along a parabolic curve, transitions seamlessly into constant velocity, then decelerates smoothly along another parabolic curve back to zero velocity.

The acceleration goes from infinity (raw straight line) to a finite, constant value — a dramatic improvement.

Matching Cycloidal Curves to Constant Velocity

The matching procedure for cycloidal curves is identical to that for parabolic curves. This works because parabolic and cycloidal motion have the same maximum velocity for equal rise and lift angle.

The advantage of using cycloidal matching over parabolic matching is the same as before: at high speeds, the smooth acceleration changes of cycloidal curves produce lower actual dynamic forces.

The Computation Process

For a composite displacement diagram with a parabolic rise, constant velocity mid-section, and parabolic deceleration, the process is:

1. Determine the total rise h and total angle β
2. Divide the angle into three segments: acceleration angle, constant-velocity angle, and deceleration angle
3. Apply the matching formula — for parabolic matching:

$$y = 2h_1\left(\frac{\phi}{\beta_1}\right)^2$$

where h₁ is the rise during the acceleration phase and β₁ is the corresponding angle. The formula must satisfy the condition that 2h₁ is substituted for h and 2φ₁ for β, so that:

$$\frac{h_1}{h_2} = \frac{\frac{1}{2}\phi_1}{\phi_2}$$

4. Calculate displacement values at regular angular intervals for the entire diagram
5. Use these values to lay out or machine the cam profile

Cam Profile Determination: From Diagram to Metal

"Now we turn the story into steel," the practitioner said.

The displacement diagram tells you what the follower must do. The cam profile is the physical shape that makes it happen. Determining the cam profile from the displacement diagram requires a clever mental trick called an inversion.

The Inversion Technique

Constructing a cam profile requires drawing many positions of the cam with the follower in its correct location for each position. But instead of rotating the cam (which is messy to draw), you fix the cam and rotate the follower around it.

This is the inversion: hold the cam still, and imagine the follower orbiting around it.

Critical rule: The artificial rotation of the follower must be the reverse of the cam's prescribed rotation. If the cam rotates counterclockwise, the follower positions are drawn clockwise.

Profile Construction for a Radial Translating Roller Follower

Step-by-step process:

1. Draw a circle of radius R_min (the minimum radius from cam center to pitch curve, which is the path of the roller center)
2. Divide the circle into angular increments matching the displacement diagram (typically every 2° to 10°)
3. Number these positions according to the cam rotation sequence, but in the reverse direction
4. At each angular position, mark a radial distance from the cam center equal to R_min + y, where y is the displacement value from the diagram at that angle
5. Connect these points with a smooth curve — this is the pitch curve (the path of the roller center)
6. Draw circles of radius r_f (the roller radius) at each point on the pitch curve
7. The cam profile is the inner envelope of all these roller circles

Profile Construction for a Swinging Roller Follower

The construction is similar but accounts for the arc of the swinging arm:

1. Establish the pivot point M and the cam shaft center
2. The displacement h is stepped off on an arc drawn with M as center
3. For each angular position of the cam, rotate the pivot point M around the cam shaft center (in the reverse direction of cam rotation)
4. From each pivoted position, draw an arc of radius L_f (the follower arm length) between the R_min and R_max circles
5. Step off the displacement diagram ordinate along each arc
6. Connect the points to form the pitch curve
7. Draw roller circles and find the envelope

If the total swing angle φ₀ is known, the displacement h is found from:

$$h = \frac{\pi \phi_0 L_f}{180°}$$

Pressure Angle and Radius of Curvature: The Two Gatekeepers

the practitioner drew a single diagram that would reshape how the practitioner thought about cam design forever.

What Is the Pressure Angle?

The pressure angle at any point on a cam profile is the angle between:

• The direction the follower wants to go (the tangent to the follower's path)
• The direction the cam pushes it (the line perpendicular to the cam profile tangent at the point of contact)

In an ideal world, the cam would push the follower exactly in the direction it needs to go (pressure angle = 0°). In reality, there is always some angular mismatch, and this mismatch has consequences.

Why the Pressure Angle Matters

Increasing the pressure angle:

• Increases the side thrust on the follower and its guides
• Increases friction forces in the follower bushings
• Can cause the follower to jam or bind in its guides
• Increases the force required from the cam to produce the same follower motion

But decreasing the pressure angle means increasing the cam size, which brings its own problems:

• Larger cam = larger machine footprint
• More precise manufacturing required (higher cost)
• Higher circumferential speeds = deviations from theoretical path cause acceleration proportional to the square of the cam size
• More revolving mass = increased vibration
• Greater inertia = difficulty with quick starting and stopping

Maximum Allowable Pressure Angles

The engineering community has established guidelines through decades of practice:

These values are conservative. Many applications successfully exceed them, but beyond these limits, a detailed force and stress analysis is mandatory.

Graphical Method for Determining Cam Size (Translating Follower)

The graphical method allows you to design a cam with a specified maximum pressure angle:

1. From the displacement diagram, identify the two points P₁ and P₂ having the maximum angles of slope (τ₁ and τ₂)
2. Calculate the constant k from the displacement diagram length:

$$k = \frac{L}{2\pi}$$

where L is the horizontal length of the displacement diagram representing 360°.

3. Determine the values k·tan(τ₁) and k·tan(τ₂) by geometric construction
4. Lay out the stroke h vertically with the displacement values y₁ and y₂ marked
5. Draw rays at the specified maximum pressure angles α₁ and α₂
6. The intersection zone of these rays defines the area A — any point within this area chosen as the cam shaft center will produce a cam whose pressure angles at P₁ and P₂ do not exceed the specified values

Key design insight: Choosing the cam center at the intersection of the two rays (point O₁) yields the smallest possible cam for the given requirements. This typically requires an offset follower with offset distance e.

If a radial follower (zero offset) is preferred, choose the cam center on the follower's line of motion (point O₂). This may change one of the pressure angles.

Formulas for Calculating Pressure Angles

For standard cam profiles with radial translating roller followers:

Constant Velocity Motion:

$$\alpha = \arctan\frac{180°h}{\pi\beta R_\alpha}$$

$$\alpha_{max} = \arctan\frac{180°h}{\pi\beta R_{min}} \quad \text{(occurs at } \phi = 0°\text{)}$$

$$R_{min} = \frac{180°h}{\pi\beta\tan\alpha_{max}}$$

Parabolic Motion (first half, 0 ≤ φ ≤ β/2):

$$\alpha = \arctan\frac{720°h\phi}{\pi\beta^2 R_\alpha}$$

$$\alpha_{max} = \arctan\frac{360°h}{\pi\beta R_\alpha} \quad \text{(occurs at } \phi = \beta/2\text{)}$$

Simple Harmonic Motion:

$$\alpha = \arctan\left(\frac{90°h}{\beta R_\alpha} \cdot \sin\frac{180°\phi}{\beta}\right)$$

The angle φ_p where maximum pressure angle occurs:

$$\phi_p = \frac{\beta}{180°} \cdot \text{arccot}\left(\frac{\beta}{180°}\tan\alpha_{max}\right)$$

Cycloidal Motion:

$$\alpha = \arctan\left(\frac{180°h}{\pi\beta R_\alpha}\left(1 - \cos\frac{360°\phi}{\beta}\right)\right)$$

Radius of Curvature: Preventing Undercutting and Failure

The radius of curvature of the cam profile is the second critical gatekeeper. If it becomes too small, catastrophic problems arise.

What Happens When the Radius of Curvature Gets Too Small

Three scenarios illustrate the progression from acceptable to catastrophic:

Scenario A — Normal operation (ρ_min > r_f): The radius of curvature of the pitch curve (ρ) is larger than the roller radius (r_f). The actual cam surface has a smooth convex radius of curvature:

$$R_c = \rho - r_f \quad \text{(convex surface)}$$

Scenario B — Knife edge (ρ_min = r_f): The cam surface radius of curvature becomes zero. The cam has a sharp corner at this point. Surface stresses become extreme and the cam will fail rapidly.

Scenario C — Undercutting (ρ_min < r_f): This is physically impossible. The cam profile would need to curve more sharply than the roller can follow, causing undercutting. The actual follower motion will deviate from the intended displacement diagram. The cam cannot be manufactured as designed.

Minimum Radius of Curvature Formulas

The general formula for radius of curvature:

$$\rho = \frac{\left(r^2 + \left(\frac{dr}{d\phi}\right)^2\right)^{3/2}}{r^2 + 2\left(\frac{dr}{d\phi}\right)^2 - r\frac{d^2r}{d\phi^2}}$$

where r is the distance from the cam center to the pitch curve at angle φ.

For Parabolic Motion (deceleration portion, β/2 ≤ φ ≤ β):

$$r = R_{min} + h - 2h\left(1 - \frac{\phi}{\beta}\right)^2$$

$$\frac{dr}{d\phi} = \frac{720°h}{\pi\beta}\left(1 - \frac{\phi}{\beta}\right)$$

$$\frac{d^2r}{d\phi^2} = \frac{-4(180°)^2 h}{\pi^2\beta^2}$$

ρ_min can occur at either φ = β/2 or φ = β. Calculate both and take the smaller value.

For Simple Harmonic Motion:

$$r = R_{min} + \frac{h}{2}\left(1 - \cos\frac{180°\phi}{\beta}\right)$$

$$\frac{dr}{d\phi} = \frac{180°h}{2\beta}\sin\frac{180°\phi}{\beta}$$

$$\frac{d^2r}{d\phi^2} = \frac{(180°)^2 h}{2\beta^2}\cos\frac{180°\phi}{\beta}$$

Again, ρ_min can occur at either φ = β/2 or φ = β.

For Cycloidal Motion:

$$r = R_{min} + h\left(\frac{\phi}{\beta} - \frac{1}{2\pi}\sin\frac{360°\phi}{\beta}\right)$$

$$\frac{dr}{d\phi} = \frac{180°h}{\pi\beta}\left(1 - \cos\frac{360°\phi}{\beta}\right)$$

$$\frac{d^2r}{d\phi^2} = \frac{2(180°)^2 h}{\pi\beta^2}\sin\frac{360°\phi}{\beta}$$

$$\rho_{min} = \frac{\left(R_{min} + 0.91h\right)^2 + \left(\frac{180°h}{\pi\beta}\right)^2)^{3/2}}{(R_{min} + 0.91h)^2 + 2\left(\frac{180°h}{\pi\beta}\right)^2 + (R_{min} + 0.91h)\frac{2(180°)^2 h}{\pi\beta^2}}$$

(ρ_min occurs near φ = 0.75β for cycloidal motion.)

Worked Example: Comparing Minimum Radii of Curvature

Given: h = 1 unit, R_min = 2.9 units, β = 60°

Key insight: Cycloidal motion produces the smallest minimum radius of curvature. This is the trade-off for its superior acceleration characteristics. The designer must ensure R_min is large enough to prevent undercutting.

Rules for Concave Cam Surfaces

Undercutting cannot occur at concave portions of the cam profile. However, to enable milling or grinding of concave sections, the cam's radius of curvature must be:

$$R_c = \rho_{min} + r_f > r_{cutter}$$

where r_cutter is the radius of the milling cutter or grinding wheel.

Cam Forces: The Physics of Making Metal Move

With the displacement diagram designed and the pressure angle and radius of curvature checked, it was time for the practitioner to learn about forces — the invisible loads that determine whether a cam survives or fails.