Research ArticleINDUSTRIAL ROBOTS

The milliDelta: A high-bandwidth, high-precision, millimeter-scale Delta robot

See allHide authors and affiliations

Science Robotics  17 Jan 2018:
Vol. 3, Issue 14, eaar3018
DOI: 10.1126/scirobotics.aar3018
  • Fig. 1 The milliDelta: a millimeter-scale Delta robot.

    Design of the milliDelta is based on origami-inspired engineering and made using PC-MEMS manufacturing techniques. The robot is driven by three piezoelectric bending actuators. Power and control signals were delivered via a five-wire tether. (A) The milliDelta with components labeled. Perspective views of the milliDelta moving through its workspace near the top (B), bottom (C), left (D), and right (E) with externally powered light-emitting diode for visualization.

  • Fig. 2 Schematic representation of the milliDelta.

    Revolute joint axes are labeled with dashed black lines. The composite laminate structure is shown with mechanical components as described in the legend. The milliDelta has two parallel plates (the fixed base and the output stage) that are connected by three kinematic chains, each consisting of base arm and parallelogram linkages. Three additional input transmission linkages were added to convert and amplify (by 1/L3) the bending motion (red arrow) of the actuators to rotary motion at the fixed base (black arrow). Cross-sectional views of input transmission linkages are shown in upper (A), neutral (B), and lower (C) configurations with flexible polyimide layer as shown in the legend. (D) Universal joints conventionally present at the fixed base and at the output stage were approximated with two perpendicular revolute joints separated by distance Dra. Assembly flexural joints fixed at an angle of 45° were introduced to keep the moving flexural joints unloaded at the center of the milliDelta’s workspace.

  • Fig. 3 Workspace comparison of Delta robots.

    A comparison of (A) a conventional Delta robot design (Dra = 0 mm), (B) the milliDelta (Dra = 0.8 mm), and (C) a Delta robot with 2× axis bias (Dra = 1.6 mm). The xy projection of the workspaces is shown in (D), and the xz projection is shown in (E).

  • Fig. 4 Experimental characterization of the milliDelta’s quasi-static workspace (yellow) compared with the theoretical workspace (blue) generated by the kinematic model.

    Outlines of the xy and xz projections of the workspaces are shown in (A) and (B). The 18 trajectories shown in (C) and (D) outline the extent of the workspace with actuator input amplitudes selected to avoid collision between linkages for all trajectories. (E) Experimental blocked force measurements in the vertical (z) direction as a function of vertical distance from the center of the workspace. The stiffness increased as the millDelta approached the extent of its workspace. Error bars indicate 1 SD.

  • Fig. 5 Magnitude response, |H(jω)|, of the milliDelta’s output stage for small perturbations in the Cartesian directions (rows) for each arm (columns).

    The estimated linear system is shown in blue, and experimental magnitude response is shown in orange. Resonant modes, with the addition of a tracking marker, were between 75 and 95 Hz.

  • Fig. 6 Quasi-static and dynamic trajectories.

    Left: Quasi-static (1 Hz) experimental (orange) and desired (blue) trajectories for a 0.5-mm-length planar circle (A), star (B), and H (C). Control inputs were determined by using the kinematic model. Right: High-bandwidth experimental (orange) and desired (blue) trajectories for a 0.5-mm-length star executed at 20 Hz (D) and a 1.5-mm-diameter circle executed at 75 Hz (E). Control inputs were determined by using the estimated linear dynamic model.

  • Fig. 7 Experimental results for tremor reduction.

    Orthogonal camera views used to record hand tremors (A) and milliDelta motion (B) are shown with a red circle denoting the tracked point. (C) Tremor data for two individuals are shown with bounding ellipsoids. The linear model was inverted offline to allow the milliDelta to track the measured tremors, and the tracking error is shown with bounding ellipsoids (D). The milliDelta was able to reduce hand tremor magnitudes by 81% RMS.

  • Fig. 8 Experimental setup for workspace, bandwidth, and force characterization of the milliDelta.

    Two orthogonal, synced, high-speed cameras were centered on the milliDelta. A reflective marker was placed on the output stage, and its position was tracked by using vision-based techniques. For force testing, a single-axis force sensor that obscured the top camera was positioned above the milliDelta. The cameras, force sensor, and milliDelta were controlled in real time by using MATLAB’s xPC target system.

  • Table 1 Relevant parameters for a selection of currently available Delta robots.
    DeviceSize (mm)Weight (g)Workspace (mm3)Frequency (Hz)Payload (N)Accuracy (μm)
    IRB 360 FlexPicker (35)565 radius
    1000 height
    120,000~3.5 × 108~3~78100
    Adept Quattro s650HS (35)650 radius
    1150 height
    117,000~6.6 × 1085~59100
    Pocket Delta (35)171 × 171 × 2705.6~4.8 × 10520.23
    Laminated Delta robot (16)~100 ×100 ×100~7001100
    milliDelta15 × 15 × 200.4307.01750.01315
  • Table 2 Trajectory following results.

    RMS precision and accuracy are calculated over five cycles of data recorded at 100 fpc.

    TrajectoryFrequency
    (Hz)
    Length
    (μm)
    RMS precision
    (μm)
    RMS accuracy
    (μm)
    Circle15002.3 ± 1.134.9 ± 0.1
    Star15001.9 ± 0.524.7 ± 0.2
    H15002.4 ± 0.833.2 ± 0.2
    Star205005.2 ± 0.968.6 ± 0.4
    Circle7515004.3 ± 1.4211.9 ± 1.4

Supplementary Materials

  • robotics.sciencemag.org/cgi/content/full/3/14/eaar3018/DC1

    Fig. S1. Relevant linkage parameters for one arm of the milliDelta.

    Fig. S2. Manufacturing process for the milliDelta.

    Fig. S3. Singular value plot of the transfer function matrix as a function of frequency.

    Table S1. Link length parameters of the milliDelta, piezoelectric bending actuator dimensions, and flexure stiffnesses.

    Movie S1. High-frequency motion.

    Movie S2. Trajectory following.

    Movie S3. Tremor compensation.

    Reference (51)

  • Supplementary Materials

    Supplementary Material for:

    The milliDelta: A high-bandwidth, high-precision, millimeter-scale Delta robot

    Hayley McClintock,* Fatma Zeynep Temel,* Neel Doshi, Je-sung Koh, Robert J. Wood*

    *Corresponding author. Email: hayley.mcclintock{at}wyss.harvard.edu (H.M.); fztemel{at}seas.harvard.edu (F.Z.T.); rjwood{at}seas.harvard.edu (R.J.W.)

    Published 17 January 2018, Sci. Robot. 3, eaar3018 (2018)
    DOI: 10.1126/scirobotics.aar3018

    This PDF file includes:

    • Fig. S1. Relevant linkage parameters for one arm of the milliDelta.
    • Fig. S2. Manufacturing process for the milliDelta.
    • Fig. S3. Singular value plot of the transfer function matrix as a function of frequency.
    • Table S1. Link length parameters of the milliDelta, piezoelectric bending actuator dimensions, and flexure stiffnesses.
    • Reference (51)

    Download PDF

    Other Supplementary Material for this manuscript includes the following:

    • Movie S1 (.mp4 format). High-frequency motion.
    • Movie S2 (.mp4 format). Trajectory following.
    • Movie S3 (.mp4 format). Tremor compensation.

    Files in this Data Supplement:

Navigate This Article