Robotic Manipulator Reach vs Stroke: Understanding the Relation

In robotics, understanding the specifications of a manipulator is key to knowing its capabilities. Two fundamental specifications are 'Reach' and 'Stroke'. Let's break down what they mean and how they relate.

Defining Robotic Manipulator Reach

The Reach of a robotic manipulator refers to the maximum distance its end-effector (the tool or gripper at the end of the arm) can extend from the robot's base or mounting point. It essentially defines the outer boundary of the robot's working envelope, indicating the furthest point in space the robot can possibly touch.

Defining Robotic Manipulator Stroke

The Stroke typically relates to the maximum linear displacement or travel distance of a specific component within the manipulator, most commonly a prismatic joint or a linear actuator. It quantifies how much a linear element can extend or retract.

Analyzing the Reach vs. Stroke Relationship

Consider how these two specifications interact:

• The Reach is the ultimate maximum distance from the base to the end-effector.
• The Stroke is the maximum linear travel of a particular part, often one that contributes to extending the robot's arm.

If a robot arm uses a linear actuator or a prismatic joint with a specific stroke (let's call it S) to achieve its maximum extension, the reach (let's call it R) depends on this stroke. Assuming the base is at a fixed point, the maximum distance the end-effector can reach is influenced by this stroke.

In many configurations:

• The maximum reach R can be exactly equal to the stroke S, if the stroke is the sole factor determining the extension from the base. For example, if a robot arm extends purely along a linear axis starting from the base, and the axis has a stroke S, the reach is S.
• Alternatively, the overall reach R might be limited by other factors, such as the lengths of other connected links or the limits of rotational joints. In such cases, the reach R could be less than the stroke S.

It is generally not possible for the stroke S to be greater than the reach R, because the stroke represents the maximum travel of a component *contributing* to the reach. The reach is the final measured distance, which cannot exceed the maximum possible extension capability provided by its components.

Therefore, the most accurate general relationship is that the stroke is less than or equal to the reach.

Mathematically, this relationship is expressed as:

Stroke ${\le}$ Reach

This inequality covers both scenarios: where the stroke directly determines the reach (Stroke = Reach) and where other factors limit the total reach to be less than the available stroke (Stroke > Reach is not possible, so Stroke ≤ Reach implies Stroke = Reach or Stroke < Reach).