Kinematics Terminology Related to Parallel Mechanisms

Position Analysis

Pose: The position and orientation of the mobile platform.

Configuration: The combined positions and orientations of all links and the mobile platform.
Similar Terms: posture.

Articular coordinates: The variables describing the actuated joints.
Similar Terms: articular variables, input variables, control variables.

Generalized coordinates: The variables describing the pose of the mobile platform.

Inverse kinematics: The problem of finding the articular coordinates from the generalized ones.
Similar Terms: inverse kinematic problem, reverse kinematics.

Direct kinematics: The problem of finding the generalized coordinates from the articular ones.
Similar Terms: direct kinematic problem, forward kinematics.

Working mode: One of the several solutions of the inverse kinematic problem.

Assembly mode: One of the several solutions of the direct kinematic problem.

Velocity (Singularity) Analysis

Inverse instantaneous kinematics: The problem of finding the articular velocities from the generalized ones.

Direct instantaneous kinematics: The problem of finding the generalized velocities from the articular ones.

Singular configuration: A configuration in which the complete instantaneous motion of the mechanism (all joint velocities) cannot be determined from either the articular velocities or from the generalized velocities.

Workspace Analysis

To alleviate the following definitions, let point C be an arbitrary point fixed to the mobile platform. Also, all the points from a given workspace subset correspond to the same assembly mode of the parallel robot, i.e., the parallel manipulator can move continuously between any two points from a given workspace subset, without having to be disassembled.

Complete workspace: The set of all attainable poses of the mobile platform (i.e., a 6D entity in the case of 6-DOF parallel manipulators).

Workspace subset: A subset of the complete workspace.

Constant-orientation workspace: The set of all positions that can be attained by point C when the mobile platform is kept at a constant orientation.
Similar Terms: translational workspace, positioning workspace, output accessible set.

Orientation workspace: The set of all attainable orientations of the mobile platform for point C being fixed to a particular position in the base frame.

Projected orientation workspace: The set of all attainable directions of a vector fixed in the mobile frame for point C being fixed to a particular position in the base frame.

Maximal workspace: The set of all positions that can be attained by point C for at least one orientation of the mobile platform. Similar Terms: reachable workspace.

Dextrous workspace: The set of all positions that can be attained by point C with any orientation of the mobile platform.

Physical envelope: The set of all points that can be attained by at least one point from the whole parallel mechanisms in at least one configuration.

Dynamic workspace: The set of all attainable poses and accelerations of the mobile platform. This notion pertains to parallel mechanisms actuated by cables.