How to Solve the Challenges of Torque Measurement

With the expansion of collaborative robots into manufacturing environments, the issue of safe motion is an ongoing concern. At present, design features employed to address this issue include adding force sensors, torque sensor and at times, proximity sensors.

Image Credit: Celera Motion

In combination with more complex software control algorithms, these additions slow operation and offset the majority of concerns. However, the installation of supplementary sensors significantly increases cost and complexity of designs.

This technical paper examines the employment of calibrated motor current and internal compliance in harmonic gearing to offer a virtual torque sensor without the addition of torque sensing components.

Knowledge of the internal compliance of the mechanical structure, along with the motor torque characterization, can offer two virtual torque sensors. The virtual torque sensors within each joint may work in conjunction with one multi-degree of freedom force sensor on the robot, allowing for a reduction in expenditure and complexity while ensuring the necessary safe operation.

Selective Compliance Articulated Robot Arm (SCARA) robots engage numerous motorized robot joints. Each robot joint includes a drive motor, gear system and encoder. Highly integrated designs are being driven by the global need to reduce size, weight and complexity.

A lack of rotation stiffness is a key downside to this electro-mechanical system. This is largely a result of the zero backlash harmonic gearing employing a flexure to transmit motion.

Mechanical stiffness (or lack of stiffness) has a direct effect on the dynamic performance and accuracy of any system. The issue is worsened when cantilevered arm extensions are coupled to a motorized joint, as the load can differ greatly with each robot pose.

The output of the joint may move without movement at the input (motor) side of the joint. This torsional windup affects both dynamic performance and accuracy. Material about the stiffness characteristics as a function of load can be freely obtained from the gear suppliers.

Some studies indicate that with appropriate manufacturing processes and lubrication, the non-linear aspects of compliance are repeatable over the useful life of the gearing.

A torque transducer is a torsional spring with a measurement system that can identify the twist and offer an output. A brushless permanent magnet synchronous electric motor yields torque in proportion to the current.

Each robot joint has an encoder, with the majority of collaborative robots now offering dual encoders. As such, each joint is now able to measure torque through both the measured twist and the motor current versus torque.

The torsional spring function and the torque versus current function are both measurable and repeatable. During the manufacturing process, it is necessary to calibrate each function to remove assembly variances and normal tolerances.

While temperature changes do result in some limitations, they are typically below 2% within normal collaborative robot environments.

Robot Joint Design

A highly integrated robot joint design generally employs a direct drive motor, (large diameter and short length) coupled to high ratio gearing. As the output speed is comparatively low, generally 50-500 rpm, the gear set is worth the trade off to move the motor power peak to a greater speed and maximize the torque density and efficiency.

The best solution for torque and size is a direct drive motor coupled to a high ratio low profile gear system, and this has become the industry standard. It is worth noting that there are alternative direct drive approaches, but these are only viable for very low weight, light payload systems, such as semiconductor wafer processing.

Harmonic gear solutions are becoming the ideal alternative for high ratio gearing in more compact robots, due to their light weight, low profile, and zero backlash. Ratios in the 50-150:1 range are typically employed, with higher ratios (up to 300:1) also available.

The greatest issue with harmonic gearing solutions is that they are based on a flexure that transmits the motion between the input and the output. While this flexure is advantageous to circumvent backlash, it adds to low rotary stiffness in comparison to the tooth-to-tooth contact of typical gears.

Although a designer can switch to a larger harmonic gear solution to improve stiffness, this generally leads to a larger and heavier device. It is also possible that the larger size gearing may also be excessive for the application. As such, it is preferable to retain the small size and low weight, and to compensate for the stiffness, using this repeatable torsional spring as a virtual torque sensor.

Simultaneous measurement of the input and output joints offers sufficient data to have a closed-loop algorithm around stiffness, which can eliminate its negative effects and measure the torque at the same time.

The image below shows an example of a Celera Motion robot joint with a slotless frameless motor kit, a harmonic gear solution, and dual encoders, (one on the input and one on the output).



Image Credit: Celera Motion

The above cross-section describes the key mechanisms of a Celera Motion dual encoder robot joint. The constituents include:

Source: Celera Motion

Slotless Brushless PM Frameless Motor ImageForArticle_1048_15801041844882536.png
Zero Backlash Gearing ImageForArticle_1048_15801041894047519.png
Input & Output Absolute Encoder ImageForArticle_1048_15801041945162003.png
Fail Safe Permanent Magnet Brake ImageForArticle_1048_15801041990298504.png


For additional information on slotless motors and robot joint design guidelines, please see Celera Motion Technical Notes TN-3301, TN-3101, TN-2001.

Stiffness and Gearing

Traditional robot kinematic movements allow loads and reflected inertia to fluctuate significantly with differing robot poses. Each joint’s stiffness is a non-linear phenomenon that is dependent on load, direction and position.

A lack of stiffness results in windup between the joint’s drive motor and the joint’s output. This lingering loading must be overcome before the motor control algorithm can report signals to robot controller about any external forces applied to the robot arm.

Understanding and modeling stiffness will also offer great improvements to throughput, adding to the control loop corrections and improving bandwidth. The plot below displays measured data from a harmonic gear set. It pinpoints the lost angle when torque is applied, as well as further hysteresis that is dependent on the direction of motion and load.

Torsional Stiffness as a Function Torque andAngle.

Figure 1. Torsional Stiffness as a Function Torque andAngle. Image credit: Cone Drive

Included in the plot is a piecewise linear approximation for the non-linear aspects of this curve. However, the equation does not include the hysteresis effects based on motion direction.

A cooperative research effort by Harmonic Drive and Universiteit Leuven Celestijnenlaan in Belgium led to a technical paper that offered a complete mathematical model for the lost motion proportional to load, including the hysteresis. The model offers 95% accuracy and may be incorporated into an algorithm in a motion controller to detect load based on position differences.

One potential issue is the repeatability of this torsional spring over the life of the gearing. The following graph indicates that while other attributes of the harmonic gearing vary over the useful life, as long as it is properly lubricated, the stiffness characterization does not vary.

This data was available from a joint technical paper ESTL, ESR Technology, Harmonic Drive AG, SSA/ESTEC Netherlands.

Figure 2. This data was available from a joint technical paper ESTL, ESR Technology, Harmonic Drive AG, SSA/ESTEC Netherlands. Image Credit: Celera Motion

Two Virtual Torque Sensors = One Physical Sensor

The employment of a torque sensor at the joint output is the ideal solution for torque sensing. However, as previously noted, this option can be bulky and expensive. The data above points to two other options which allow for the sensing of torque inside the robot joint without the need for a physical torque sensor.

Virtual Torque Sensor #1

One way to sense torque is to employ dual encoders with model for gearing stiffness/hysteresis. The phenomenon is repeatable and both encoders are already present in the assembly. An algorithm in the motor controller that identifies direction, and encoder difference is all that is required. A simple test following assembly can pre-calculate the equation constants and characterize the gearing.

Virtual Torque Sensor #2

Sinusoidal FOC (field oriented control) of motor current coupled to the cog-less slotless motor offers repeatable torque output based on phase current measurements.  However, the absolute accuracy of the torque value under these conditions varies with published motor parameter tolerance, which is typically +/- 10%.

It is possible to tighten this variability and offer improved accuracy in the use of motor current as a torque sensor through a simple measurement of the actual torque constant after robot joint assembly. The final accuracy is dependent on measurement conditions.

For the majority of applications, a pair of virtual torque sensors could be used in place of a physical torque sensor. The response of these virtual torque sensors could result in more rapid robot motion, as the torque control and the encoder signals are controlled at much higher bandwidths than many strain gage-based torque sensors. The collaborative robot would then need just a single multi-degree of motion force sensor.

Torque Measurement – Summary

In the majority of instances, force detection is employed to make a robot more collaborative. If an external force is applied to the robot (by a human, for example) it is perceived by a series of sensors, which enable the controller to determine an alternative response. This response may be to cease motion, reduce speed, reduce force output, or alter direction.

The two main methods employed in collaborative robots today for detection and measurement of force or torque are load cells and motor current. The above technical paper introduces a third potential torque measurement system, employing dual encoders and a math model for the harmonic gearing system.

The above note also suggests that a simple parameter test following robot joint assembly may improve motor torque accuracy. The employment of these two virtual torque sensing options may remove the need for a physical load cell based torque sensor, along with the related expenditure and complexity.

This information has been sourced, reviewed and adapted from materials provided by Celera Motion.

For more information on this source, please visit Celera Motion.


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