507 Ways to Move Part 11: Cams, Followers & Eccentrics

1. Cam Types

1.1 Plate / Disk Cam

The most common cam type: a flat plate whose edge profile determines follower motion. The follower rides on the outer contour (or an inner groove) as the cam rotates. Brown illustrates plate cams in movements #95-97 and #149-150.

1.2 Barrel / Cylindrical Cam

A barrel cam has a groove machined into the surface of a cylinder. As the cylinder rotates, a follower pin rides in the groove, producing axial motion (parallel to the cylinder axis). This converts rotation into linear translation along the rotation axis — the principle behind many textile machines, sewing machines, and automated tools.

Brown's movements #117 and #276 show cylindrical cam arrangements. The groove can produce any desired axial displacement profile per revolution, and if the groove is a helix, the result is uniform translation (like a lead screw, but smoother).

1.3 Face / End Cam

A face cam has its profile machined on the end face of a rotating disc. The follower moves axially (along the rotation axis) rather than radially. Face cams are compact and useful where radial space is limited. They appear in indexing mechanisms, some valve actuators, and precision instruments.

1.4 Conjugate & Globoidal Cams

A conjugate cam uses two cam profiles working in opposition to positively drive the follower in both directions — no spring needed. A globoidal cam (also called a roller-gear cam or Ferguson drive) has a three-dimensional surface that engages multiple rollers on a turret, producing precise indexing motion. Globoidal cams are the gold standard for high-speed, high-accuracy indexing in packaging and assembly machines.

2. Follower Types

2.1 Knife-Edge, Roller & Flat-Face Followers

2.2 Translating vs Oscillating Followers

Translating followers move in a straight line (up/down or side-to-side). They are classified as in-line (follower axis passes through cam center) or offset (follower axis is displaced from cam center, which reduces side thrust). Oscillating (swinging) followers pivot on a fixed point and sweep through an arc — common in automotive valve trains where a rocker arm swings to open a valve.

3. Cam Profile Design

3.1 Motion Programs — Dwell-Rise-Dwell-Return (DRDR)

A cam's motion program specifies what the follower does during each angular segment of one revolution. The most common pattern is DRDR:

• Dwell (D): Follower remains stationary — cam profile is a circular arc centered on the rotation axis.
• Rise (R): Follower moves outward (or upward) — cam radius increases according to a chosen motion law.
• Dwell (D): Follower remains at maximum displacement.
• Return (R): Follower moves back to the starting position — cam radius decreases.

3.2 Cam Motion Laws: Uniform, SHM, Cycloidal & Polynomial

import math

def cam_profile_generator(h, beta_deg, motion_law="cycloidal", n_points=360):
    """
    Generate cam follower displacement, velocity, and acceleration
    for common motion laws.

    h: total follower lift (mm)
    beta_deg: angle of rise (degrees)
    motion_law: 'uniform', 'shm', 'cycloidal', 'polynomial_345'
    n_points: number of calculation points

    Returns: lists of (theta, displacement, velocity, acceleration)
    """
    beta = math.radians(beta_deg)
    results = []

    for i in range(n_points + 1):
        theta = beta * i / n_points
        theta_deg = math.degrees(theta)
        ratio = theta / beta  # normalized angle 0..1

        if motion_law == "uniform":
            s = h * ratio
            v = h / beta
            a = 0.0  # (infinite at endpoints in reality)

        elif motion_law == "shm":
            s = h / 2 * (1 - math.cos(math.pi * ratio))
            v = (h * math.pi / (2 * beta)) * math.sin(math.pi * ratio)
            a = (h * math.pi**2 / (2 * beta**2)) * math.cos(math.pi * ratio)

        elif motion_law == "cycloidal":
            s = h * (ratio - math.sin(2 * math.pi * ratio) / (2 * math.pi))
            v = (h / beta) * (1 - math.cos(2 * math.pi * ratio))
            a = (2 * math.pi * h / beta**2) * math.sin(2 * math.pi * ratio)

        elif motion_law == "polynomial_345":
            # 3-4-5 polynomial: s = h*(10r^3 - 15r^4 + 6r^5)
            r = ratio
            s = h * (10*r**3 - 15*r**4 + 6*r**5)
            v = (h / beta) * (30*r**2 - 60*r**3 + 30*r**4)
            a = (h / beta**2) * (60*r - 180*r**2 + 120*r**3)

        results.append((theta_deg, s, v, a))

    return results

# Generate profiles for comparison
h = 20.0   # 20 mm lift
beta = 120  # 120 degrees of rise

for law in ["shm", "cycloidal", "polynomial_345"]:
    profile = cam_profile_generator(h, beta, law, n_points=6)
    print(f"\n--- {law.upper()} Motion Law ---")
    print(f"{'Angle':>8} {'Disp(mm)':>10} {'Vel':>10} {'Accel':>10}")
    for theta, s, v, a in profile:
        print(f"{theta:8.1f} {s:10.3f} {v:10.3f} {a:10.3f}")

3.3 Pressure Angle & Curvature

The pressure angle is the angle between the direction of the follower's motion and the normal to the cam surface at the point of contact. A large pressure angle means a large side force on the follower guide, increasing friction and wear:

• Maximum recommended: 30 degrees for translating followers; 35 degrees for oscillating followers.
• Reducing pressure angle: Increase the base circle radius, increase the rise angle, use an offset follower, or choose a motion law with lower peak velocity.
• Minimum radius of curvature: Must be positive everywhere (convex) for flat-face followers, and must exceed the roller radius for roller followers to avoid undercutting.

4. Eccentrics

4.1 The Circular Eccentric as a Simple Cam

An eccentric is a circular disc (or cylindrical shaft section) mounted off-center. It is the simplest possible cam — its profile is a perfect circle, but because the center of rotation does not coincide with the center of the circle, it produces simple harmonic motion in a follower.

Brown's movements #89-91 show eccentrics driving various followers. The eccentricity (offset distance) equals half the stroke: stroke = 2e, where e is the distance between the rotation center and the disc center.

4.2 Applications in Machinery

Eccentrics were the dominant motion-conversion mechanism of the steam age, predating precision-machined cams:

• Steam engine valve gear: Eccentrics on the crankshaft operated slide valves (Stephenson, Walschaerts gear). Each eccentric provided near-SHM to time the steam inlet and exhaust.
• Punch presses: An eccentric on the flywheel shaft drives the ram through a connecting rod — the press stroke is simple harmonic.
• Vibrating screens and feeders: Eccentric shafts create the vibration that moves material across screens or along feeder troughs.
• Scroll compressors: An eccentric-driven orbiting scroll creates the compression chambers.

5. Valve Timing & Camshafts

5.1 DOHC, SOHC & OHV Configurations

5.2 Variable Valve Timing (VVT)

Modern engines adjust cam timing dynamically for better performance, efficiency, and emissions:

• VVT-i (Toyota) / VANOS (BMW): Hydraulically phased cam sprocket that advances or retards the entire cam by 30-50 degrees relative to the crankshaft.
• VTEC (Honda): Two cam profiles per valve — a mild lobe for low RPM economy and an aggressive lobe for high RPM power. A pin locks the rocker arms together to switch profiles at a preset RPM.
• MultiAir (Fiat/Stellantis): Eliminates the intake cam entirely, using an electrohydraulic actuator to control valve lift and timing continuously.
• Camless engines (experimental): Solenoid or pneumatic actuators replace the camshaft entirely, allowing fully programmable valve events. Research prototypes from Freevalve (Koenigsegg) demonstrate the concept.

6. Historical Context

7. Case Studies

Exercises & Self-Assessment

Conclusion & Next Steps

Cams, followers, and eccentrics give mechanical designers the power to program arbitrary motion profiles into rotating shafts. Here are the key takeaways from Part 11:

• Cam types range from simple plate cams to sophisticated globoidal indexers; each suits different motion requirements and spatial constraints.
• Follower selection (roller, flat-face, etc.) directly affects contact stress, pressure angle, and cam profile constraints.
• Motion laws (SHM, cycloidal, polynomial) determine the dynamic performance — cycloidal and polynomial are preferred for high-speed applications due to zero-acceleration boundaries.
• Pressure angle must stay below 30 degrees (translating) or 35 degrees (oscillating) to avoid excessive side forces.
• Eccentrics are the simplest cam — a circle mounted off-center — producing pure simple harmonic motion.
• Automotive camshafts represent the most ubiquitous cam application, with VVT systems providing the flexibility that a fixed cam profile cannot.