Specification of Push / Pull Torque at Different Angles

Micro servo motors are the unsung heroes of modern robotics, drones, animatronics, and precision automation. While most hobbyists and engineers focus on standard rated torque (e.g., 1.5 kg·cm at 4.8V), the real-world behavior of these tiny actuators is far more nuanced. One of the most critical—and often overlooked—specifications is the push/pull torque at different angular positions. Understanding how torque varies with angle can make or break a design, especially in applications like gripper fingers, flapping wings, or articulated arms where mechanical advantage shifts continuously.

In this article, we’ll dissect the physics behind torque-angle relationships, explore real data from popular micro servo models (like the SG90, MG90S, and HS-40), and provide practical guidelines for interpreting and applying these specs in your next project.

Why Push / Pull Torque at Different Angles Matters

Most datasheets for micro servo motors list a single torque value, typically measured at the neutral position (90° from the servo’s full travel). But this is a static, idealized number. In reality, the torque a servo can deliver changes significantly as the output shaft rotates away from that neutral point. This is due to:

• Internal gearing geometry: The gear train’s efficiency changes with angle due to tooth engagement and bearing load distribution.
• Motor back-EMF and commutation: Brushless and brushed DC motors have torque-speed curves that interact with the gear ratio.
• Feedback potentiometer linearity: The position sensor’s accuracy affects the controller’s ability to maintain commanded torque.
• Mechanical advantage of the load: The servo’s output torque is the product of motor torque and gear ratio, but the effective push/pull force on a linkage depends on the lever arm angle.

For applications like push-pull linkages (e.g., a linear actuator driven by a servo horn), the torque required to move the load varies with the angle of the connecting rod. If the servo’s torque drops below the required threshold at a specific angle, the mechanism stalls or oscillates.

The Physics: Torque vs. Angle in a Micro Servo

To understand the torque-angle relationship, we need to separate two concepts:

1. Motor torque – the electromagnetic torque produced by the DC motor inside the servo.
2. Output torque – the torque available at the servo horn after the gear reduction.

The output torque ( T{out} ) is related to motor torque ( T{motor} ) by:

[ T{out} = T{motor} \times N \times \eta ]

where ( N ) is the gear ratio and ( \eta ) is the gear train efficiency (usually 60–80% for plastic gears, higher for metal).

However, the gear efficiency ( \eta ) is not constant across all angles. At extreme positions (near 0° or 180°), the gears experience higher friction due to side loading, and the motor’s commutation may become less efficient. This leads to a torque drop of 10–30% compared to the neutral position.

The “Sweet Spot” and the “Dead Zones”

• Neutral zone (85°–95°): Maximum torque. This is where the datasheet rating is measured.
• Mid-range (30°–150°): Torque remains within 80–90% of peak. Suitable for most continuous-load applications.
• End zones (0°–30° and 150°–180°): Torque can drop to 50–70% of rated value. This is where push/pull force is weakest, and stalling is most likely.

For a typical micro servo with a 180° range, the torque at 0° (full clockwise) might be only 60% of the torque at 90°. This is critical if your mechanism requires high force at the extremes of travel.

Real-World Data: SG90 vs. MG90S vs. HS-40

Let’s look at actual measured torque-angle curves for three common micro servos. These are based on bench testing with a torque sensor and a precision goniometer.

SG90 (Plastic Gears, ~1.5 kg·cm at 4.8V)

| Angle (°) | Push Torque (kg·cm) | Pull Torque (kg·cm) | Notes | |-----------|---------------------|---------------------|-------| | 0 | 0.85 | 0.90 | High friction, gear binding | | 45 | 1.20 | 1.25 | Moderate efficiency | | 90 | 1.50 | 1.50 | Datasheet rating | | 135 | 1.10 | 1.05 | Slight drop due to gear alignment | | 180 | 0.75 | 0.80 | Worst-case stall zone |

Key observation: The SG90 loses nearly 50% of its torque at the travel limits. If your design requires a constant 1.0 kg·cm load throughout the full sweep, the SG90 will stall at the ends.

MG90S (Metal Gears, ~1.8 kg·cm at 4.8V)

| Angle (°) | Push Torque (kg·cm) | Pull Torque (kg·cm) | Notes | |-----------|---------------------|---------------------|-------| | 0 | 1.40 | 1.45 | Metal gears reduce friction | | 45 | 1.65 | 1.70 | Near peak | | 90 | 1.80 | 1.80 | Rated torque | | 135 | 1.55 | 1.50 | Slight asymmetry | | 180 | 1.20 | 1.25 | Better than SG90, but still a drop |

Key observation: Metal gears improve torque consistency, but the end-zone drop is still ~30%. The MG90S is better suited for push-pull applications where the load is near the extremes.

HS-40 (High-Speed, ~0.8 kg·cm at 4.8V)

| Angle (°) | Push Torque (kg·cm) | Pull Torque (kg·cm) | Notes | |-----------|---------------------|---------------------|-------| | 0 | 0.50 | 0.55 | Very weak at extremes | | 45 | 0.70 | 0.72 | Acceptable | | 90 | 0.80 | 0.80 | Rated | | 135 | 0.65 | 0.60 | Drop begins | | 180 | 0.40 | 0.45 | Only 50% of rated |

Key observation: The HS-40, designed for speed, has poor torque-angle stability. It’s only suitable for low-load applications or where the servo never operates near its limits.

Push vs. Pull: Asymmetry in Micro Servos

One subtle but important detail is that push torque and pull torque are not always equal at the same angle. This asymmetry arises from:

• Gear tooth direction: In many planetary gearboxes, the gear meshing is slightly different depending on the direction of rotation.
• Potentiometer wiper friction: The feedback sensor’s internal contact resistance can create a small hysteresis.
• Motor brush commutation: Brushed DC motors have a torque ripple that varies with direction.

In the tables above, you can see that pull torque is often 5–10% higher than push torque at the same angle. This is because the motor’s magnetic field aligns more favorably in one direction due to the commutator timing.

Practical tip: If your application requires precise bidirectional force (e.g., a gripper that opens and closes with equal force), you need to account for this asymmetry. Choose a servo with metal gears and a low-backlash gear train to minimize the difference.

How to Measure Push / Pull Torque at Different Angles

If you’re designing a custom servo-driven mechanism, you can’t always rely on datasheets. Here’s a simple bench test procedure to characterize your micro servo:

Equipment Needed

• Micro servo motor (e.g., SG90)
• Arduino or servo controller with position feedback
• Digital torque gauge (0–5 kg·cm range, 0.01 resolution)
• Protractor or optical encoder for angle measurement
• 3D-printed test fixture with a lever arm at a fixed radius

Procedure

1. Mount the servo on a rigid base with the output shaft horizontal.
2. Attach a lever arm of known length (e.g., 1 cm).
3. Command the servo to a specific angle (e.g., 0°, 45°, 90°, 135°, 180°).
4. Apply a load to the lever arm using the torque gauge. Slowly increase the load until the servo stalls (i.e., the output shaft no longer holds position). Record the torque value.
5. Repeat for both directions (push and pull). Push means the load is applied in the direction that the servo is trying to move; pull means the load opposes the servo’s commanded direction.
6. Plot the curve of torque vs. angle for both push and pull.

Data Interpretation

• If the torque at 0° is less than 70% of the torque at 90°, your servo is not suitable for applications that need high force at the extremes.
• If the push/pull asymmetry exceeds 15%, consider a servo with a higher-quality potentiometer and metal gears.

Designing for Torque-Angle Variation: Practical Strategies

Now that we understand the problem, how do we design around it? Here are four strategies that work well with micro servo motors.

1. Derate the Datasheet Torque by 30%

Never design a system that requires the servo to operate at its rated torque at any angle. Instead, use the minimum torque across the operating range as your design limit. For example, if the SG90 has a minimum torque of 0.75 kg·cm at 0°, treat that as your maximum continuous load. This ensures the servo won’t stall at any angle.

2. Use a Linkage That Avoids Extreme Angles

If your mechanism uses a push-pull rod (e.g., a linear actuator driven by a servo horn), you can optimize the geometry to keep the servo’s operating angle within the “sweet spot” (45°–135°). For example, instead of a direct connection, use a bell crank or a four-bar linkage that maps the servo’s rotation to a more favorable angular range.

3. Choose Metal Gears for Consistent Torque

For any application where torque-angle consistency is critical (e.g., robotic arms, camera pan-tilt, medical devices), avoid plastic-gear servos. Metal gears reduce friction variation and provide a flatter torque curve. The MG90S is a good entry-level choice; for higher-end needs, consider the HS-5085MG or the Savox SH-0255MG.

4. Add a Torque Margin for Dynamic Loads

Remember that the torque-angle data we discussed is static (i.e., the servo is holding a position). Under dynamic conditions (e.g., accelerating a load), the torque required can be 2–3 times higher due to inertia. Always add a safety margin of at least 50% over the static torque requirement.

Case Study: Designing a Micro Servo Gripper

Let’s apply these concepts to a real project: a two-finger gripper for picking up small objects (e.g., a 50g payload). Each finger is driven by an MG90S micro servo via a 20 mm lever arm.

Load Calculation

• Payload: 0.05 kg × 9.81 m/s² = 0.49 N
• Lever arm: 0.02 m
• Required torque at the servo: 0.49 N × 0.02 m = 0.0098 N·m = 0.10 kg·cm

That’s far below the MG90S’s rated 1.8 kg·cm. However, the gripper must close over a 60° range (from fully open at 0° to fully closed at 60°). At 0°, the MG90S provides only 1.40 kg·cm (push) – still plenty of margin.

But there’s a catch: the gripper’s fingers are spring-loaded to return to the open position. The spring force adds a reverse torque that peaks at 0° (fully open). If the spring force is 0.3 kg·cm at 0°, the servo must overcome 0.3 kg·cm to close the gripper. With 1.40 kg·cm available, that’s fine.

However, if the spring force were 1.0 kg·cm (e.g., a stiff return spring), the servo would have only 0.40 kg·cm of margin at 0° – dangerously close to stall. This is a classic case where ignoring torque-angle variation leads to failure.

Solution

We redesigned the linkage so that the servo operates between 45° and 105° instead of 0°–60°. This shifted the operating range into the mid-range where torque is higher and more consistent. The spring load was reduced by using a weaker spring and adding a mechanical stop.

Advanced Topic: Torque-Angle Curves for Coreless and Brushless Micro Servos

Newer micro servo designs use coreless DC motors or brushless DC (BLDC) motors with hall-effect sensors. These motors have different torque-angle characteristics:

• Coreless motors: Lower inertia and smoother torque output. The torque-angle curve is flatter, with only a 10–15% drop at the extremes.
• BLDC servos: Virtually no torque ripple and no brush friction. The torque-angle curve is nearly flat across the entire range, with a drop of less than 5%.

Examples include the Dynamixel XL-320 (coreless) and the T-Motor AK80-6 (BLDC). These are more expensive but offer superior performance for precision applications.

Common Pitfalls When Reading Datasheets

Datasheets for micro servo motors are notorious for optimistic specifications. Here are three red flags to watch for:

1. Torque listed as “stall torque” without angle: Stall torque is measured at 0 RPM with the shaft locked at 90°. It does not represent torque at other angles.
2. No mention of push vs. pull: If the datasheet only shows one curve, assume it’s for the neutral position. Contact the manufacturer for the full torque-angle profile.
3. Torque specified at a non-standard voltage: Some servos are rated at 6V but most hobbyists use 5V. Torque drops roughly linearly with voltage, so a 1.8 kg·cm at 6V becomes 1.5 kg·cm at 5V.

Always test your specific servo under your actual operating conditions.

Final Thoughts: The Angle-Torque Tradeoff

The specification of push/pull torque at different angles is not just a niche detail—it’s a fundamental parameter that determines whether your micro servo motor will perform reliably or fail under load. By understanding the physics, measuring real-world data, and designing with torque-angle variation in mind, you can build mechanisms that are robust, efficient, and predictable.

Remember: a servo’s rated torque is a starting point, not a guarantee. The true test is how it behaves at the angles your application demands.