Multi-Axis Errors in Precision Mechanical Design

Precision Mechanical Design: Multi-Axis Errors

Introduction to Multi-Axis Systems

  • Multi-axis systems are crucial in precision mechanical design, but they introduce various assembly errors that impact performance.

  • These systems often involve multiple linear or rotary axes, which must be precisely aligned.

  • A visual representation shows a primary coordinate frame (+Xa, +Ya, +Za) along with a secondary axis (+X_2), highlighting the complexity involved.

Examples of Multi-Axis Systems

  • Stacked Linear Positioning Systems: These involve multiple linear stages mounted atop each other to achieve motion in several directions. (A YouTube link was provided as an example resource: http://www.youtube.com/watch?v=kWPvYE2qetU)

  • Gantry Systems: Characterized by a structure that spans over a workspace, enabling high-precision, large-travel motion. Examples include AEROTECH CARTESIUS-SO and AERO systems.

  • Parallel Kinematic Systems: These systems use multiple kinematic chains connecting the base to the end-effector, offering high stiffness and accuracy. (U.S. Patents 4760094 and 6671975 were referenced).

  • Nested Goniometers: These devices provide precise angular positioning, often stacked to achieve multi-axis rotational movement.

  • Industrial Robots: Such as the FANUC M-900, exemplify complex multi-axis systems used for automated manufacturing tasks.

Measuring Machines for Error Assessment

  • Coordinate Measuring Machines (CMMs): Used to measure the physical geometrical characteristics of an object.

  • Roundness Measuring Instruments: For example, the Mitutoyo Roundtest 12-5050, specifically designed to evaluate the roundness and cylindrical form of components.

Types of Assembly Errors

Various errors can occur during the assembly of multi-axis systems, significantly affecting their precision and functionality:

  • Squareness

  • Parallelism

  • Offset

  • Coaxiality

  • Orientation (Alignment)

Detailed Definition of Assembly Errors

Squareness Error

  • Definition: Refers to the deviation from 90 extdegree from which two axis average lines are aligned, as defined by ISO 230-1.

  • Nomenclature:

    • An error term like ECOY indicates the squareness error.

    • The first subscript (C, A, B) denotes the axis about which the reference axis average line is rotated.

    • The second subscript (O, E) indicates the axis being rotated.

    • The third subscript (X, Y, Z) indicates the axis that the axis average line is rotated about.

    • The fourth subscript (X, Y, Z) indicates the rotated axis.

  • Six Linear Axis Squareness Terms:

    • ECOY – squareness of Y to X

    • ECOX – squareness of X to Y

    • EAOY – squareness of Y to Z

    • EAOZ – squareness of Z to Y

    • EBOX – squareness of X to Z

    • EBOZ – squareness of Z to X

Parallelism Error

  • Cases:

    • Linear motion and an axis of rotation: The angle between the reference straight line of the trajectory of the functional point of a linear moving component and the axis average line of a rotating component.

    • Two axes of rotation: The angle between the axis average line of two rotating components.

  • Evaluation: This error is assessed in two orthogonal planes.

Offset Error

  • Definition: An error in the physical location of a rotary axis average line relative to the defined reference coordinate frame.

Orientation Error

  • Definition: An error in the angular alignment (orientation) of the rotary axis average line with respect to the reference coordinate frame.

Coaxiality Error

  • Definition: Describes both the offset at a specified location and the angle between two nominally coaxial axis average lines, as per ISO 230-1.

  • Evaluation: Similar to parallelism, it is evaluated in two orthogonal planes.

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