Motion control analysis of miniature gantries

Inside Machines: Looking at the static and dynamic characteristics of miniature parallel kinematic gantries can help determine selection of the best technology. Motion applications include 3D printing, screw driving, glue dispensing, and light assembly. Criteria include application requirements for travel, throughput, moving weight, smoothness of motion, and static precision.


Figure 1: Microplate positioning as shown in “Principles of Fluorescence Spectroscopy, 3rd edition,” edited by Joseph R. Lakowicz, provided as courtesy by Springer.An increasing need for desktop automation tools is noticeable in numerous markets. Examples of life science applications include: film scanners, DNA analyzers, inkjet printers, assaying, and lab automation.

Other desktop automation needs are found in light assemblies, such as screw driving, glue dispensing and 3D printing. A process tool for such applications consists of a frame, positioning system, controller, human machine interface (HMI), and a tool. A common constraint for all desktop tools is limited space. This requirement implies miniature components and small parts, all packaged in a confined space. The resulting design objective is to maximize the ratio of the working XY travel to footprint. Other positioning requirements include moving load, process throughput, smoothness of motion, settling time, positioning accuracy, and cost.

Analysis of the static and dynamic characteristics of a miniature parallel kinematic gantry shows it is a cost-effective option for desktop automation tools because of its characteristic frequencies, static precision, dynamic precision, and high-performance frequency response capabilities.

3D printers, labs, light assembly

Desktop automation tools are gaining popularity in lab automation and light assembly applications. Such applications may require both high static and dynamic precision for the process application. They also may require high acceleration and high velocity (conflicting needs), for high throughput. The combination of high throughput with the required precision should be at a low-enough cost to justify the return on investment of the motion technology selected.

Conflicting requirements, of high precision at high throughput, are very noticeable in applications that require many small step-and-repeat moves or one move with smooth motion. An example of step-and-repeat applications is shown in Figure 1. The example shows a moving microplate, which makes many small steps in XY directions by using stationary sensor optics. To reach high throughput in such an application requires high acceleration and high jerk. However, high jerk excites many resonance frequencies of the positioning stage, which may in turn vibrate the microplate. These vibrations also may prolong settling time, thus reducing the throughput, or distort the optical image, which may in turn lower the imaging precision.

Similarly, applications that require smoothness of motion, such as inkjet printing, may have a conflict with high velocity. While smooth motion requires minimal disturbances, to reach high velocity within a short travel requires high jerk. High jerk raises the acceleration to high values in a short time, but also may result in a velocity overshoot, which in turn prolongs the time it takes to settle to the desired constant velocity.

The motion system design needs to know the root causes of internal system vibrations to ensure that induced system vibrations do not interfere with process needs.

A miniature gantry analysis follows. 

Miniature gantry tests

Figure 2: Miniature, parallel kinematics gantry. Courtesy: FestoMiniature belt-driven gantries, as shown in Figure 2, have a unique H-shaped configuration, making them attractive for desktop automation tools. Main advantages, compared with compounded, cantilever XY stages or split axes, are as follows:

  • A large ratio of working envelope to footprint due to low-profile XY axes maximizes the work envelope in a very limited desktop space.
  • Two stationary servo or stepper motors for X and Y stages reduces the moving weight, eliminates the Y-axis moving cables, reduces inertial loads, increases reliability, and reduces cost.
  • Integration to small desktop frame at high or low elevation easily can be adapted to the spatial process constraints.
  • Simple construction with minimal motion components implies high reliability and lower downtime.
  • Modularity suits application in a transfer line, where many sequential units perform simultaneous process work along a long line of processed parts.

These features of miniature parallel kinematics stages increase reliability, simplify integration and programming, and reduce material cost, making the miniature gantry an attractive candidate for desktop automation processes. 

Mini gantry test plan, test configuration

Figure 3: A typical metrology test shows a typical worst-case (Y-axis) results of the mini H. Courtesy: FestoFor the purpose of testing mini gantry characteristics, a standard Festo Mini H gantry EXCM-30 with X, Y travel of 370 x 762 mm was chosen. The gantry was securely mounted to a test bench, with a 1.8 Kg moving load. A laser interferometer was used for precision testing at 100 mm Abbe offset above the Y slide. The stage tension was calibrated with an electronic "tuning fork" to its standard specification. Tests were done using two of Festo's stepper motors, EMMS-ST, with rotary encoders, and two servo amplifiers, EXCM-2ST.

In addition, a second set of tests was done with the mini H using Tamagawa servo motors and ACS SPiiPlus NTM08080808YYY, high-performance motion controller, including UDMmc4H4N0YN drive with 5/10 A and 48 V dc bus. These tests were done without and with a 1.62 kg load. Frequency response testing was done using a motion controller from ACS Motion Control. 

Test procedure

Testing included:

  • Static precision. Moving to desired position. Record accuracy (uncalibrated), unidirectional repeatability, bi-directional repeatability.
  • Dynamic characteristics. Tapping the stage. Record position bandwidth, servo damping, and holding position jitter.
  • Dynamic precision. Moving the stage in 500 mm/sec and sample position error at 1 kHz. Record resonant and disturbance frequencies, velocity variation, settling time to constant velocity, at the end of the acceleration phase, settling time to various accuracy windows at the end of the deceleration phase. 

Static precision

Static precision was:

  • Accuracy 730 um [noncorrected]
  • Accuracy 300 um [with 2 endpoint correction]
  • Unidirectional repeatability +/- 8 um
  • Bi-directional repeatability +/- 80 um.

As shown, the limiting precision characteristic of the mini gantry is its hysteresis, which affects the bi-directional repeatability. This is a typical limitation of a belt-driven stage with motor encoder. During a direction change the motor starts moving, and the encoder starts reading position changes. The belt then starts stretching, yet without any axis slide motion, until the belt tension overcomes the static friction of the slide. Only then the axis slide starts its motion while lagging behind the indicated encoder reading.

The low bi-directional repeatability limitation may not be an issue in desktop applications where a process is always in one direction—for example, in a screw driving system, when a screw is always being picked up in one direction and being placed on an object, such as a printed circuit board (PCB), always in the opposite direction. In such a case, the repeatability of picking up the screw and placing it on the PCB will always be at a uni-directional value.

If, on the other hand, the process is in two directions, then bi-directional repeatability may be improved, as needed, by adding a linear encoder to the axis. The linear encoder will not be insensitive to the belt stretch and will react only to the slide motion. This is a nonstandard option some mini gantries.

Figure 4: This shows X stage frequencies. Courtesy: FestoFigure 4 shows a typical frequency spectrum of the Festo Mini H gantry. Initial observation showed three distinct regions, yet without a clue to their root cause. Of great interest was the close proximity of the lowest two modes.

To explain these frequencies, the natural frequency in X and Y translation was estimated using Fn = sqrt (k/m)/ (2 *л). FEA was used to estimate the bending modes of the Y stage, and the belt string vibration was measured as a reference. 

Observed frequencies were then correlated with the calculated frequencies of the various vibration modes. The results were found to be in close enough proximity to make the following conclusions:

  • The first two modes are the X and Y translation. They are in close proximity due to a similar ratio of belt stiffness and moving load.

Fnx = sqrt (160000/3)/6.28 = 36.8 Hz
Fny = sqrt (109000/1.8)/6.28 = 39.2 Hz 

  • The third and fourth modes were correlated Y-axis yaw and the Y-axis bending, respectively, as shown in Figure 5. 

Figure 5: This shows third mode Yaw (43 Hz) and fourth mode bending (78 Hz) of Y stage. Courtesy: FestoThe other frequencies are most likely higher modes of vibrations of the Y stage as well as timing belt engaging pulley grooves, ball jitter of the recirculating rails, and belt string vibrations.

Notice that the lowest three natural frequencies in the mini gantry are the most critical for precision control. They are the sharpest, have the largest amplification, and are the main limiting factors of position bandwidth. Bandwidth position is the key to high dynamic accuracy, smoothness of motion, and low settling time, and it is typically on the order of 1/3 of the lowest natural frequency.

Table 3 presents the dynamic precision test results of the mini H with Tamagawa standard servo motors and ACS servo controller / amplifier (load 1.62 kg). Note that optimized dynamic performance may be possible in applications where the load is constant.

As shown in Figure 6, the mini gantry dynamic performance may be optimized to an order of magnitude higher performance, using high-performance servo motors and motion controllers including bi-quad and notch filters. Figure 7 results show 159 Hz bandwidth for the Y stage, at 38 degrees phase margin and 15 db gain margin. Table 3 results show the respective maximum dynamic error of the Y stage at 500 mm/s, 1 g and 1.68 kg moving weight, is 70 um, with a steady state CV error of 21 um and a settling time to 6 um within 12 msec. 

Linear motor results, belt-driven cost

Figure 6: Frequency response of the mini H Y-axis with Tamagawa Servo Motor and ACS Controller Amplifier shows position bandwidth of 159 Hz. Courtesy: FestoThese results are, in many respects, on the same order of magnitude as linear motors stages, yet at cost of a belt driven stage.

The bi-directional repeatability of the mini H gantry is on the order of 100 um. It is affected, as expected, by the belt hysteresis. The mini H repeatability may be improved as needed, by an order of magnitude, of +/- 10 um, by using a uni-directional positioning process, or alternatively by using a custom linear encoder.

The three lowest natural frequencies range from 30 to 70 Hz. They are belt stiffness related frequencies, including X tension, Y tension, and Y yaw. The next frequencies are structural natural frequencies, between 70 and 200 Hz, including Y beam bending and torsion. The higher frequencies (of lesser importance) are most likely related to the belt string vibration, and to other vibration sources that vary with motion, such as belt / pulley interaction and recirculating bearing balls moving in and out of their grooves.

Results show that dynamic accuracy of a standard mini H gantry in a standard Festo stepper motor configuration provides settling to 10 um in 200 msec. An order of magnitude higher performance may be obtained by using servo motors and higher performance controllers, with higher order filters, such as the Tamagawa and ACS Motion Controller.

Figure 7: This is an example of a Festo standard mini H in a desktop immunoassay testing machine. Courtesy: RheonixFinally, by knowing application requirements for travel, throughput, moving weight, smoothness of motion, and static precision, the mini gantry configuration with its motion parameters may be considered as the most cost-effective solution for an automated desktop process.

For supporting test and analysis work, the author thanks Mustansir Faizullabhoy, Colin Johnson, Nick Xie, and Patrick Haran, all with Festo USA; and Jason George and Andrew Hines, with ACS Motion Control.

- Boaz Eidelberg, PhD, is with Festo customer solutions, Americas; edited by Mark T. Hoske, content manager, Control Engineering, 

Festo gantries 

Mini H gantry information: 

Festo is a CSIA member as of 3/5/2015


Key concepts

  • Motion control analysis of miniature parallel kinematic gantries can help match technology to the application.
  • Mini gantries can be used for 3D printing, screw driving, glue dispensing, and light assembly.
  • Travel, throughput, moving weight, smoothness of motion, and static precision are among application criteria.

Consider this

Testing can help match the right technologies to the motion control application. Ask for the specifications.

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