Hybrid motion–measurement control and traceable HMI for a 3-PSP manipulator

Parallel kinematic mechanisms (PKMs) remain attractive in industrial applications such as cable- and wire-driven designs that expand workspace and stiffness management (Ha et al., 2024; Sung and Joe, 2025). They are increasingly used for precision positioning in compact metrological stages because closed-loop structures can provide high stiffness, low moving mass and favourable dynamic response within a limited workspace (Russo et al., 2024). Although most industrial coordinate measuring machines (CMMs) are serial, PKM architectures are compelling where a small, rigid workspace is sufficient. The same kinematic coupling that enables stiffness introduces challenges. Workspace conditioning and proximity to singularities affect control and planning, and errors propagate through coupled geometry rather than accumulating along a chain as in Cartesian systems (Di Gregorio and Parenti-Castelli, 2001; Russo et al., 2024; Zhang et al., 2024a).

The 3-prismatic–spherical–prismatic (3-PSP) topology is a well-studied translational PKM with an analytical formulation that supports implementation in micro-manipulation and micro-metrology (Di Gregorio and Parenti-Castelli, 2001). Prior work introduced a 3-PSP micro-CMM and developed its kinematic and error models, establishing a mechanical and analytical foundation for metrological application (Rugbani and Schreve, 2015). Recent surveys underline that achieving high absolute accuracy in PKM and small-scale CMM platforms depends on coordinated advances in control, calibration and error compensation rather than mechanics alone (Geng et al., 2021; Zhang et al., 2024a). This reinforces the need to document software and control choices that directly shape measurement quality.

Touch-trigger probing is commonly adopted in compact systems because it is simple and repeatable, yet measurement quality depends on approach kinematics, contact angle, stylus compliance and local contact mechanics. These factors determine pre-travel behaviour at trigger and can introduce direction- and speed-dependent effects that must be controlled in software (Bastas, 2020; Rępalska and Woźniak, 2022; Sepahi-Boroujeni et al., 2020; Sun et al., 2023). Standardising approach vectors, creep-in speeds and trigger handling within the control software improves repeatability and helps to bound systematic effects that are not fully captured by geometric error models. These aspects are critical to metrological performance because they govern how trajectories are generated and verified, including force/position handling under delays that arise in practical systems (Wu et al., 2024).

Despite extensive research on PKMs for precision positioning and coordinate metrology, existing studies have predominantly focused on mechanical architecture, kinematic modelling and geometric calibration techniques (Di Gregorio and Parenti-Castelli, 2001; Rugbani, 2026; Russo et al., 2024; Zhang et al., 2024b). By contrast, the role of software-level control logic, probing orchestration and execution-aware traceability management in shaping metrological performance has received comparatively limited systematic treatment, particularly for compact PKM-based coordinate measuring systems.

In this context, the present work introduces a hybrid motion–measurement control architecture for a 3-PSP micro-CMM that explicitly couples iterative closed-loop kinematic reconciliation with deterministic stop-on-trigger probing. Unlike conventional PKM probing approaches that rely on open-loop motion execution until contact, the proposed strategy continuously reconciles inverse- and direct-kinematic estimates prior to probing, thereby reducing residual pose error and stabilising the approach trajectory at contact. Related synchronised and coupled control strategies have been shown to improve positioning stability in PKM-based stages; however, their integration with probing logic and metrological measurement workflows has remained largely unexplored (Jana et al., 2023a; Jana et al., 2023b).

Furthermore, a traceability-oriented human–machine interface (HMI) is developed in which metrological provenance, including commanded setpoints, sensor states, trigger events and operator actions, is embedded directly within the control software. This design departs from conventional PKM and robotic metrology systems where traceability is typically addressed offline or treated as an external data-management task and instead aligns with contemporary guidance that emphasises transparent, execution-level documentation as a prerequisite for defensible coordinate measurement and uncertainty analysis (Kniel et al., 2019; Barbosa et al., 2022).

Lastly, the proposed system is experimentally validated against a calibrated industrial CMM using agreement analysis, rather than nominal error reporting alone. By quantifying bias, dispersion and limits of agreement, the evaluation situates the system within established metrological assessment practice and clarifies that observed accuracy limitations are primarily attributable to geometric calibration residuals and workspace sensitivity, rather than deficiencies in controller dynamics (Bland and Altman, 1986; Geng et al., 2021). Taken together, these elements reposition the reported system from a device-specific engineering implementation to a reproducible software and control template for PKM-based micro-metrology platforms, with direct relevance to robotic inspection and intelligent measurement systems.

The instrument adopts a 3-PSP parallel architecture in which three identical limbs, each sliding on a runner block mounted with spherical joints, the limbs are rigidly connected to a moving triangular platform. Three linear actuators are mounted vertically to control limb displacement. The arrangement yields three translational degrees of freedom of the probe in the laboratory frame while maintaining high structural stiffness and low moving mass. The global coordinate system is defined with the origin at the base-frame centroid; the z-axis is vertical, and x–y lie in the base plane. All geometric parameters are provided in prior work (Rugbani and Schreve, 2015, 2017). The micro-CMM design and a schematic drawing of the machine are shown in Figure 1.

Analytical formulations of the forward and inverse kinematics have been validated in earlier studies (Rugbani and Schreve, 2015), providing a reliable foundation for real-time computation within the control software. Similar translational PKMs have been investigated in recent work for ultra-precision positioning and micro-assembly, demonstrating sub-micrometre repeatability when properly calibrated and thermally stabilised (Mussatayev et al., 2021; Barbosa et al., 2022). These findings support the suitability of the 3-PSP topology for hybrid motion–measurement applications.

Each limb is actuated by a precision linear stage that forms the prismatic joint. Absolute position estimation does not depend solely on motor encoders; three laser displacement sensors continuously measure distances from fixed reference points on the structure to corresponding points on the moving platform. The controller fuses these readings through the direct-kinematics model to estimate the probe position (x, y, z) in real time, a strategy consistent with recent manipulator studies that integrate sensing and control for enhanced precision (Zhang et al., 2024a; Wu et al., 2024). A touch-trigger probe mounted on the platform provides a digital contact signal used both to stop motion and to record the measurement point.

All transducers interface with a computer through a National Instruments data-acquisition layer that enables synchronous sampling and deterministic event handling. Continuous monitoring of sensor data allows the software to detect contact events and apply safety interlocks promptly. This integration of sensors and actuators establishes a fully observable control loop suitable for traceable measurement operations.

For metrological traceability, the control software records commanded setpoints, timestamped sensor data, computed probe poses, trigger events and operator actions. The resulting audit trail supports reproducibility and provides the data basis for later uncertainty analysis. Maintaining such comprehensive logs conforms with current guidance on traceability in dimensional metrology, which emphasises transparent documentation of measurement conditions, sensor states and instrument configurations (Kniel et al., 2019).

The control system is organised into three cooperating modules that execute concurrently through well-defined software interfaces. Movement control generates and refines actuator commands to realise requested Cartesian setpoints while respecting workspace and stroke limits. Measurement control supervises touch-trigger events and executes a deterministic stop-and-capture sequence that preserves the contact state for coordinate computation. Display and logging provide live state feedback to the operator and maintain a comprehensive audit trail for traceability. The software is implemented in LabVIEW with embedded Python kernels for computational routines for the forward and inverse kinematics, thereby combining rapid hardware integration with numerically robust kinematic evaluation (Johra, 2019; National Instruments, 2018).

The architecture adopts a hybrid motion–measurement strategy that couples iterative closed-loop positioning with open-loop stop-on-trigger capture. Iterative positioning reduces residual pose error prior to contact by reconciling inverse-kinematic setpoints with direct-kinematic estimates derived from laser displacement readings. Stop-on-trigger capture minimises disturbance at the instant of contact and reflects established practice in coordinate metrology with touch-trigger systems, where approach kinematics and trigger handling directly affect repeatability (Bastas, 2020; Sepahi-Boroujeni et al., 2020).

An overall software flowchart illustrates how the movement, measurement and logging components interact, see Figure 2. In essence, the software cycles through reading sensors, solving kinematics, moving motors and logging events in a deterministic loop, with high-priority branching for probe triggers and safety interlocks.

Conventional PKM-based probing systems typically execute motion in open loop until a trigger event occurs, at which point the measured pose is inferred directly from encoder or sensor readings. In such configurations, residual inverse-kinematic errors and kinematic coupling effects are not actively corrected during the approach phase and may influence contact conditions, particularly in regions of reduced workspace conditioning. The hybrid control strategy adopted in this work introduces iterative reconciliation between inverse- and direct-kinematic estimates prior to probing, providing a systematic means to bound pre-contact pose error and stabilise approach conditions. Similar synchronised feedback concepts have been shown to improve convergence stability in PKM positioning stages; however, their explicit integration with probing and measurement capture remains limited in the literature (Jana et al., 2023a; Jana et al., 2023b).

The movement controller’s objective is to place the probe at a desired Cartesian setpoint p = (x, y, z) while respecting the mechanism’s workspace limits, avoiding singular configurations and staying within the actuator stroke limits. The controller uses the inverse kinematics model (IKM) to compute nominal leg extensions z_a, z_b, z_c required to place the platform at the target P. The controller then executes a sequential leg-by-leg positioning routine with continuous sensor feedback. Moving the legs one at a time permits solving the IKM and reduces kinematic cross-coupling for this 3-PSP system (Rugbani and Schreve, 2017). The coordinate system is shown in Figure 3.

The probing sequence proceeds as follows:

• The IKM solver takes the desired Cartesian coordinates (x, y, z) and computes the corresponding leg extensions z_a, z_b, z_c for the three linear actuators. These computed values are the ideal lengths each leg should have to place the probe at P. The solver will reject targets that violate stroke or lie outside the workspace envelope.

• Compute the required leg displacements (dz) for target position P. The controller moves one leg at a time, applying corrections before moving the next. Start with leg A: command motor A to move to the calculated z_a position, while motors B and C remain fixed. Then, read the three laser sensors to get the current distances l_a, l_b, l_c and recompute the actual extension of leg A achieved; if the error exceeds a threshold, the controller commands motor A again by the error amount and repeats the sensor reading and comparison. Iterate until dz_a is within tolerance. Repeat for legs B and C.

• Cartesian verification. Compute achieved pose P′ from DKM. If P′−P exceeds tolerance, perform a small Cartesian refinement.

When a contact is expected, the controller reduces feed in the final segment and subdivides motion to limit kinetic energy at touch; thresholds are configurable in the HMI. The block diagram for the movement control module is shown in Figure 4, and the LabVIEW movement algorithm is shown in Figure 5.

When the touch-trigger probe makes contact with a surface, the system executes an immediate stop-and-capture sequence to record the measurement point. The probe trigger signal is polled in a high-priority loop, and upon detection, all motion commands are immediately inhibited. The system samples the readings of the three laser displacement sensors and runs the direct kinematics to compute the contact coordinates at trigger time. These coordinates, together with timestamps and state flags, are committed to the session data set. The probing phase is intentionally open loop after trigger. Maintaining the contact state is prioritised over further correction at the instant of touch.

The routine proceeds as follows:

• The touch-trigger probe emits a digital signal the moment it contacts the workpiece. The control software is continuously monitoring this signal in a high-priority loop.

• The motor drive commands are cut off to prevent any further motion of the probe. Due to slow approach speed, the overshoot upon trigger is minimal.

• With the probe stationary at contact. The system samples the laser readings and solves DKM to compute the contact coordinates P at trigger time.

• The coordinates P, timestamp, and relevant state flags are appended to the session data set. The user can choose to save the data set, repeat the measurement or move to the next point.

The block diagram of the measurement control procedure is shown in Figure 6.

Display and logging run concurrently with movement and measurement. The display layer streams live estimates of the probe pose and leg extensions to the HMI so that the operator can monitor convergence, interlocks and probe arming in real time. Warnings are raised when software limits or singularity margins are approached, and emergency stop events are latched for operator acknowledgement.

The logging service records all significant commands and events with monotonic timestamps. Logged items include commanded setpoints, achieved poses at verification steps, raw sensor frames at key phases, trigger events with associated state, operator actions such as jogging or manual capture. Export functions write a human-readable point list with identifiers and a machine-readable metadata file that summarises software version, calibration constants and session conditions.

Transparent documentation of measurement conditions, sensor states and configuration allows reported values to be related to standards through a documented chain of comparisons and facilitates defensible uncertainty evaluation (Kniel et al., 2019). The present implementation aligns with this guidance by coupling the user interface with deterministic logging hooks that ensure no probe event or anomaly is unrecorded. These logs provide an auditable trail that supports reproducibility and subsequent uncertainty assessment (Kniel et al., 2019). The closed-loop display control module is illustrated in Figure 7.

The HMI consolidates planning, execution and data review into a single workflow that prioritises repeatability and metrological traceability. The interface presents clear controls for entering target positions, initiating motion, arming the probing routine and exporting results. In parallel, a deterministic logging service captures software states, sensor data and operator actions to create a complete audit trail suitable for uncertainty analysis and method verification (Kniel et al., 2019).

The interface follows three principles:

1. Planning is separated from execution to reduce cognitive load.

2. Persistent visibility of system state, including live position, arming of the probing routine and limit status.

3. Actions that affect data integrity, such as recording a point or overwriting a session, require explicit confirmation and are timestamped.

In terms of layout, the HMI is implemented as a single-window LabVIEW application with multiple panels and controls logically grouped by function. This choice enables asynchronous event handling for probe triggers and emergency stops and supports custom indicators that reflect interlocks and trigger states in real time (Johra, 2019; National Instruments, 2018). Figure 8 illustrates the interface layout.

Key elements of the interface are:

• Target input: Cartesian setpoints are entered or loaded from a plan file. Inputs are validated against workspace and stroke limits prior to execution. The accepted setpoint and a timestamp are logged.

• Live pose display: The current probe position from the direct kinematics is shown continuously alongside leg extensions. This aids situational awareness and provides an immediate check on convergence.

• Measurement list: Each recorded point appears with an index, coordinates and time. Manual entries are flagged to distinguish them from touch-trigger events.

• Current position real time.

• Expect measurement toggle: Arming this control activates the slow-approach routine and the trigger handler. The state is recorded so that the intent at the time of contact is auditable.

• Record last reading: Captures the present pose without a trigger, useful for reference points or diagnostics; entries are explicitly marked as manual.

• Manual jog controls: Incremental moves are available per leg or per Cartesian direction with selectable step size. Jog actions and resulting poses can be logged to reconstruct operator interventions.

• Export and import: Data sets and session metadata are exported in Excel documented formats, and planned point lists can be imported to script repeated tasks.

• Emergency stop and interlock status. A prominent stop command halts drives immediately. Interlock states (limits, singularity proximity) are visible and timestamped when asserted.

The logging service runs continuously in the background of the HMI to record every significant event. It logs all commanded setpoints and movement initiations; the raw sensor streams at key points and all computed probe poses; each probe trigger time. Every log entry is tagged with a timestamp and identifying information for the session. This log data enables a complete reconstruction of the measurement process after the fact. For example, given the logs one can determine exactly which points were measured under “slow approach” conditions, what the probe status was and even reproduce the sequence of moves and pauses. Such detailed audit trails greatly facilitate uncertainty analysis because they allow isolation of whether an outlying point might correlate with, say, a momentary loss of laser sensor signal or an operator intervention. The comprehensive logging is thus a cornerstone of ensuring metrological traceability in this system. Data from each session are saved in both human-readable and machine-readable formats. Optionally, a full raw data log (including time-series of sensor readings and events) can be exported for deeper analysis.

To verify the effectiveness of the control and HMI software, metrological tests were conducted to observe how software-driven motion and event handling affected measurement accuracy and repeatability.

The data set comprises 25 measurements distributed within the reachable workspace. For each point, the prototype micro-CMM was driven to a commanded pose using the hybrid control routine and the touch-trigger event was captured by the measurement module. The industrial CMM (Mitutoyo Bright Apex 710) then measured the probe tip position in the laboratory frame, as illustrated in Figure 9(a). The difference between the prototype reading and the industrial CMM reading defines the pointwise positioning error. Figure 9(b) shows the spatial distribution of the points.

Each acquisition is associated with a session identifier and a full software log that records approach settings, trigger events, sensor snapshots, computed poses and operator actions. These records allow reconstruction of the motion–measurement sequence for every point and provide evidence that the same slow-approach parameters were in effect when probing was armed. Before analysis, sign conventions and coordinate frames were checked. A rigid transformation was applied where required so that both instruments are expressed in a common frame. The prototype has an existing analytical error model (Rugbani and Schreve, 2015), which is used to contextualise measured errors and to identify whether residuals reflect calibration limits or local kinematic sensitivity.

Accuracy is summarised by the absolute per-axis differences $(dx,dy,dz)$ and by the 3D Euclidean error magnitude for each point. For descriptive statistics, the study reports the mean, standard deviation, minimum and maximum of these errors across the 25 points. Axis-wise biases are also reported to reveal systematic components that may indicate residual misalignment, scale mismatch or workspace-dependent sensitivity.

Repeatability is estimated from repeated measurements at identical locations. For those points, the standard deviation of the measured coordinates provides an indicator of short-term precision under the same approach conditions. This reflects common practice in coordinate metrology and enables comparison with the expected dispersion from probe repeatability and sensor noise.

Agreement analysis is performed by a Bland–Altman plot using the radial magnitudes of the position vectors derived from the industrial CMM and from the prototype micro-CMM. The analysis reports the mean difference and the 95% limits of agreement and tests for proportional bias through a regression of difference on average (Bland and Altman, 1986).

Across the 25-point data set, the prototype micro-CMM shows sub-millimetre mean positioning error relative to the industrial CMM. Figure 10 summarises the absolute magnitudes of per-axis differences (dx, dy, dz). Larger excursions are observed at points 6, 14 and 15, driven primarily by the x-axis component (dx ≈ 1 mm). These deviations are attributed to a combination of residual frame alignment error and workspace-dependent kinematic sensitivity, whereby small geometric or scale residuals can be amplified along specific Cartesian directions depending on Jacobian conditioning. Such location-dependent error amplification is a well-documented characteristic of translational PKMs, particularly away from the workspace centre or near regions of reduced isotropy (Di Gregorio and Parenti-Castelli, 2001). Similar behaviour has also been reported in coordinate measurement studies where residual calibration errors interact with approach direction and local geometry (Mazur et al., 2022). Overall, the y and z components exhibit smaller biases and moderate spread, while the x-axis carries most of the systematic offset, consistent with the absence of geometric error compensation in the present implementation.

The 3D Euclidean error $e=dx2+dy2+dz2$ for each point is listed in Table 1 together with summary statistics (mean, SD, min, max). The error distribution is centred below 1 mm with mean 0.656 mm, median approximately 0.53 mm, root mean square 0.73 mm and maximum 1.339 mm. Axis-wise biases were −299 µm for x, + 66 µm for y and + 169 µm for z. These values are consistent with expectations for the current platform without geometric error compensation. The observed axis-wise differences are consistent with direction-dependent point identification effects on planar features reported in controlled CMM studies (Mazur et al., 2022).

Agreement between the prototype and the industrial CMM was examined by a Bland–Altman plot constructed on the radial magnitudes of the position vectors (Bland and Altman, 1986). The radial position vectors obtained using the industrial CMM and from the prototype micro-CMM are $rref$ and $rpro$⁠, respectively, where $r=x2+y2+z2$⁠. Each point is plotted with the x-axis representing the average of the position vectors (r_ref + r_pro)/2 and the y-axis the difference r_ref − r_pro.

Across 25 measurements, the mean difference (bias) was 0.317 mm, with 95% limits of agreement from −0.404 mm to 1.039 mm. A regression of difference on average yielded a slope of approximately 0.0012 mm per mm, indicating negligible proportional bias (Bland and Altman, 1986). These results suggest small systematic offset and acceptable dispersion over the tested range of magnitudes. Figure 11 presents the plot with the mean line and limits of agreement.

The solid horizontal line shows the mean difference (bias) = 0.317 mm; dashed lines show the 95% limits of agreement (−0.404 mm, 1.039 mm). A dotted regression of difference vs average indicates negligible proportional bias (slope ≈ 0.0012).

The results indicate that the implemented control strategy delivered stable convergence to setpoints and consistent capture at contact. Absolute accuracy remained primarily constrained by geometric calibration and workspace sensitivity rather than controller dynamics. The hybrid architecture is therefore a suitable basis for further enhancement. Two immediate extensions emerge from the observed error structure. Firstly, geometric error compensation through parametric calibration or grid-based error maps is expected to reduce systematic components, particularly the dominant x-axis bias. Secondly, force-regulated probing could further reduce pre-travel variability where touch-trigger dispersion contributes to the error envelope, especially for oblique approach geometries noted in PKM stages with coupled kinematics.

It is noted that the present evaluation does not incorporate geometric error compensation, thermal modelling or force-regulated probing. Consequently, the observed absolute accuracy is primarily constrained by calibration residuals and workspace-dependent kinematic sensitivity, rather than by limitations of the proposed control architecture itself, consistent with prior observations in PKM-based and machine-tool metrology systems (Geng et al., 2021; Zhang et al., 2024b).

This study presented a hybrid motion–measurement control architecture and a traceability-oriented HMI for a 3-PSP micro-CMM. Iterative closed-loop positioning reconciled inverse-kinematic setpoints with direct-kinematic estimates before contact, while stop-on-trigger capture preserved the physical contact state for coordinate computation. The integrated HMI exposed system state, enforced controlled approach conditions and produced a comprehensive audit trail spanning setpoints, sensor snapshots, trigger events and operator actions.

Evaluation against a calibrated industrial CMM across 25 points showed sub-millimetre mean error with a maximum of approximately 1.34 mm and axis-wise biases dominated by the x component. These results indicate that absolute accuracy was limited primarily by geometric calibration and workspace sensitivity, whereas the proposed control logic and probing procedure yielded stable convergence and consistent capture.

The architecture advances PKM-based micro-metrology by demonstrating that software choices in motion sequencing, probing logic and provenance management can materially influence metrological outcomes. Deterministic logging and explicit mapping between operator actions and recorded fields support reproducible analysis and align with contemporary guidance on metrological traceability in dimensional measurement (Kniel et al., 2019). The contribution of this work lies in the integration of hybrid motion–measurement control, probing orchestration and traceability-aware data capture within a single software architecture, rather than in the development of new kinematic formulations or mechanical designs.

Two directions are expected to provide the largest gains. Geometric error compensation, implemented either through parametric calibration or grid-based error maps, should reduce systematic components observed along the x axis and narrow the overall error envelope. Force-regulated probing offers a path to further stabilise pre-travel behaviour where touch-trigger dispersion contributes to local variability.

The reported system provides a reproducible software and control template for translational PKMs intended for coordinate metrology. It can be adopted on comparable hardware without altering operator workflow, and it offers a clear pathway to higher accuracy through calibrated compensation and enhanced probing control.

This research received no specific grant from any funding agency in the public, commercial or not-for-profit sectors.

Ali Rugbani and Abdulhakim Agll: Conceptualisation, system architecture design, software development (LabVIEW–Python integration), experimental validation, data analysis, hardware setup and integration, data acquisition and calibration, Ali Rugbani: visualisation; writing – original draft; testing supervision; validation; writing, review and editing, Ali Rugbani and Abdulhakim Agll: Both authors have read and approved the final version of the manuscript.

This study did not involve human participants, animals or sensitive personal data, and therefore did not require institutional ethics approval. All experimental procedures complied with relevant institutional and safety regulations.