Units and Coordinates

Encoder Counts
(Joint Space)

The position of each principal N9 axis is continually monitored with encoders. These encoders are sensors that divide the angular or axial range of a joint into a discrete number of counts (cts). The number of counts that comprise a joint’s range varies by joint as a function its gear ratio.

Encoder counts are a joint space coordinate. This means the position (either angle or distance) of each joint is given as a single number in units of cts to express the configuration of the robot, rather than as Cartesian coordinates such as x, y, z. The argument order for positioning joints is (gripper, elbow, shoulder, z-axis), moving from the end of the arm in order of joints toward the robot’s column.

The N9’s home position is expressed as (0, 0, 0, 0) in units of cts. Counts are whole number integers, typically greater than or equal to 0 cts and less than or equal to the maximum counts in that joint’s range, shown above. The gripper joint is an exception as it has infinite rotational range in any direction and can accept any value of counts.

Radians

(Joint Space)

The position of each revolute N9 axis may also be expressed as an angle in radians (rad). Like encoder counts, radians are a joint space coordinate. However, since the z-axis is a prismatic joint, its position cannot be expressed in radians. Instead, z-axis coordinates can be given in millimeters.

Unlike when using encoder counts as coordinates, the position (0, 0, 0, 0) in rad (mm) would not home the N9. Rather, the N9 joints would align and extend outward from the lowest theoretical position on the z-axis (0 mm). In reality, the lowest possible position of the z-axis is 26 mm above the frame deck, depicted below. This limitation prevents collisions between the robot’s gripper fingers and the deck.

Cartesian Coordinates (Task Space)

The position of the gripper end-effector is referred to as task space coordinates and can be described in Cartesian coordinates (x, y, z, [θ]) relative to the system’s global Cartesian origin. The angle θ is an optionally given angle that represents the orientation of a tool when it is held by the end-effector. This angle is measured with respect to the system’s x-axis and is inconsequential if no tool is grasped in the end-effector.

The global origin of the system in Cartesian coordinates is at deck height, collinear with the axis of rotation of the shoulder. That is, if the arm could be lowered such that it touched the deck, the bottom-center of the shoulder joint would be at the global Cartesian origin. Visually, it is located at the second fastener hole visible forward of the z-axis column.

Since the robot is of a SCARA design, the (x, y) position of the end-effector is determined by the position of both elbow and shoulder joints while the height of the end-effector is directly obtained from the position of the z-axis joint. Note that for any given (x, y, z) coordinates of the end-effector, there are potentially multiple joint space configurations of the arm that can achieve that position. See IK Solutions.

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