# Manual Positioning Basics

## Basic Function and Specifications

The function of a translation stage is to constrain motion to a desired direction. For a linear stage, the desired motion is along an ideal straight line. Any motion in constrained directions will contribute to deviation from the ideal trajectory and/or position. Other contributors to deviations include load forces and everything associated with the formidable task of designing and constructing a perfect stage in a world where perfect machining and ideal materials do not exist. To put it mildly, high performance motion systems are complex, so overlooking a seemingly small issue, either in design or in an application, can produce undesirable results. Thus, the intended use of a product along with the various measures of performance must be thoroughly reviewed.
Please note: Unless otherwise stated, performance data in this catalog is on a per axis basis and are not intended to represent the performance of a stack of multiple stages. Always review stacked, multi-axis applications with a Newport applications engineer.

## Coordinate System and Sign Convention

Any positioning stage is considered to have six degrees of freedom: three linear, along the x, y, and z-axes and three rotational about those same axes (see Figure 1). All motions described here follow the right-hand coordinate system convention. The cross-product of the +X and +Y axes (pointer and middle fingers) is the +Z axis (thumb). Also if the thumb of the right hand points in the positive direction of an axis, the fingers will wrap around the axis in the direction of positive rotation about that axis. All movements are composed of translations along and/or rotations about the coordinate axes. Generally, the X and Y axes are on the horizontal plane (the direction of travel of the first or bottom stage being aligned with the X axis) and the Z-axis as vertical.

Figure 1—Right-hand coordinate system showing six degrees of freedom.

## Runout of a Linear Stage

Runout of a Linear Stage is the linear (versus angular) portion of off-axis error. It is the departure from desired, ideal straight line motion and consists of two orthogonal components. In ISO-230 and ASME B5.57 standards, runout is referred to as straightness or the lack thereof. However, in the motion industry it is common to refer to flatness and straightness as defined below.

Flatness
In Figure 2, ideal straight line motion is depicted as being confined to the x-axis. Flatness deviation is displacement along the z-axis.
Straightness
In Figure 2, ideal straight line motion is depicted as being along the x-axis. Straightness deviation is displacement along the y-axis.

Figure 2—Off-axis deviations in a linear stage.

## Tilt of a Linear Stage

Tilt of a Linear Stage is the angular deviation associated with ideal straight line motion and actual measured motion. Tilt has three orthogonal components commonly referred to as pitch, roll, and yaw (Figure 3). It can be a complex combination of the three components.

Figure 3—Roll, pitch and yaw are defined with respect to the direction of travel.

## Cross-coupling

In multi-axis systems, cross-coupling refers to a change in one axis as a result of input to another axis.

## Abbe Error

Abbe Error is the linear off-axis error introduced through amplification of tilt by an Abbe offset moment arm (Figure 4). This type of error becomes more of a problem when the point under measurement is at a relatively long distance from the axis of motion. This error will be approximately 0.02 micro-meters per 20 mm of offset per 1 micro-radian.

Figure 4—Abbe error due to measurement at an offset point. Note stage tilt.

## Eccentricity and Wobble of a Rotary Stage

Eccentricity is the radial (perpendicular to the axis of rotation) deviation of the center of rotation from its mean position as a stage rotates through one revolution (Figure 5). It is also referred to as radial runout. A perfectly centered stage with perfect bearings would have no eccentricity. Wobble is nutation, through one revolution, of the axis of rotation relative to the ideal axis (Figure 5). It is most easily observed as a cyclic tilting of the rotating surface or table top of a stage and can produce Abbe error. Like eccentricity, it is generally the result of imperfect bearings.

Figure 5—Off-axis deviations in a rotary stage.

## Cosine Error

Misalignment between the measurement axis and the axis of motion produces cosine error. This error is a function of the angle between the measurement axis and the axis of motion (Figure 6). It is eliminated when the axis of motion and the measurement axis are parallel.

Figure 6—Cosine error due to misalignment of the measuring scale with the axis of motion.

## Play

Play is the term for uncontrolled movement due to looseness of mechanical parts. Play is a contributor to backlash.

## Friction

Friction is defined as the resistance to motion between surfaces in contact. Elements contributing to friction may be in the form of drag, sliding friction, depleted lubrication, system wear or lubricant viscosity.

## Stiction

Stiction is the static friction that must be overcome to impart motion to a body at rest. Since static friction is generally greater than moving friction, the force which must be applied to impart motion is greater than the force required to keep the body in motion. As a result, when a force is initially applied, the body will begin to move with a “jump” that results in position and/or velocity overshoot. A stage design goal is to achieve static friction as close to the moving friction as possible in an effort to reduce the effect of stiction. One function of motion control electronics is to implement algorithms that reduce the impact of stiction by quickly making necessary corrections to a move profile.

## Position Stability

Position Stability is the ability to maintain a position within a specified range over time. Deviation from a stable position may also be called drift. Contributors include worn parts, vibration, migration of lubricant, and thermal variations.

Load Capacity is the maximum allowable force that can be applied to a stage, in a specified direction, while meeting stage specifications. This maximum force includes static (mass * gravity) and dynamic forces (mass * acceleration). Dynamic forces must include any external forces, such as vibrations, acting upon the stage. The amount of acceleration a stage can impart to a mass is limited to the accelerating force it can produce without exceeding a load capacity. For rotary stages, torque (the product of angular acceleration and rotational moment of inertia) is the analog of force. Rotational torques on linear stages can also be a significant factor when cantilevered loads are accelerated. Unless otherwise specified, catalog load capacities refer to a centered normal load (Figure 7).

Figure 7—Capacity specifications refer to loads that are centered and perpendicular.