Application module: Kinematic state ISO/TS 10303-1798:2018-11(E)
© ISO

Cover page
Table of contents
Copyright
Foreword
Introduction
1 Scope
2 Normative references
3 Terms, definitions and abbreviated terms
    3.1 Terms and definitions
    3.2 Abbreviated terms

4 Information requirements
   4.1 Required AM ARM
   4.2 ARM type definitions
   4.3 ARM entity definitions
   4.4 ARM subtype constraint definition
   4.5 ARM function definition
5 Module interpreted model
   5.1 Mapping specification
   5.2 MIM EXPRESS short listing

A MIM short names
B Information object registration
C ARM EXPRESS-G   EXPRESS-G
D MIM EXPRESS-G   EXPRESS-G
E Computer interpretable listings
F Change history
Bibliography
Index

4 Information requirements

This clause specifies the information requirements for the Kinematic state application module. The information requirements are specified as the Application Reference Model (ARM) of this application module.

NOTE 1  A graphical representation of the information requirements is given in Annex C.

NOTE 2  The mapping specification is specified in 5.1. It shows how the information requirements are met by using common resources and constructs defined or imported in the MIM schema of this application module.

This clause defines the information requirements to which implementations shall conform using the EXPRESS language as defined in ISO 10303-11. The following begins the Kinematic_state_arm schema and identifies the necessary external references.

EXPRESS specification:

*)
SCHEMA Kinematic_state_arm;
(*

4.1 Required AM ARM

The following EXPRESS interface statement specifies the elements imported from the ARM of another application module.

EXPRESS specification:

*)
USE FROM Kinematic_structure_arm;    --  ISO/TS 10303-1797
(*

NOTE 1   The schemas referenced above are specified in the following part of ISO 10303:

Kinematic_structure_arm ISO/TS 10303-1797

NOTE 2   See Annex C, Figures C.1, C.2, C.3and C.4 for a graphical representation of this schema.

4.2 ARM type definitions

This subclause specifies the ARM types for this application module. The ARM types and definitions are specified below.

4.2.1 ksa_initial_application_domain_enumeration   EXPRESS-G

The ksa_initial_application_domain_enumeration provides predefined identifiers for the initial application domains of Product_view_definitions.

EXPRESS specification:

*)
TYPE ksa_initial_application_domain_enumeration = ENUMERATION BASED_ON initial_application_domain_enumeration WITH
   (kinematic_state);
END_TYPE;
(*

Enumerated item definitions:

kinematic_state: the application domain is kinematic state.

4.2.2 spatial_rotation   EXPRESS-G

The spatial_rotation type allows for the designation of the data types ypr_rotation, and Rotation_about_direction.

The spatial_rotation type enables an arbitrary rotation in 3D space (R3) to be specified either as a ypr_rotation or as a Rotation_about_direction.

EXPRESS specification:

*)
TYPE spatial_rotation = SELECT
   (ypr_rotation,
    Rotation_about_direction);
END_TYPE;
(*

4.2.3 ypr_enumeration   EXPRESS-G

The ypr_enumeration is a means by which the angles of rotation about the origin in Cartesian coordinate space R3 are distinguished. The yaw represents the angle by which the original frame (x0; y0; z0) is rotated first about the z-axis to yield an intermediate (x′, y′, z′) frame. The pitch represents the angle by which the intermediate frame (x′, y′, z′) then is rotated about the y′-axis to yield another intermediate (x″, y″, z″) frame. The roll represents the angle by which the (x″, y″, z″) frame is rotated about the x″-axis to yield the desired final (x, y, z) frame.

NOTE    For more detailed information on yaw, pitch, and roll convention see ISO 8855:1991

EXPRESS specification:

*)
TYPE ypr_enumeration = ENUMERATION OF
   (yaw,
    pitch,
    roll);
END_TYPE;
(*

Enumerated item definitions:

yaw: the angle of rotation about the z-axis;

pitch: the angle of rotation about the y′-axis;

roll: the angle of rotation about the x′-axis.

4.2.4 ypr_rotation   EXPRESS-G

The ypr_rotation type is a means for specifying an ordered sequence of the angles of rotation. The yaw value is the first, the pitch value the second, and the roll value the last element in the array. The yaw rotation shall be performed first, followed by the pitch rotation. The roll rotation shall be performed as the last action of a ypr_rotation.

NOTE    An EXPRESS function which returns the rotation matrix corresponding to an input ypr_rotation is given in annex E. This function has been provided for applications that use this part of ISO 10303, but need the rotational transformation to be expressed in terms of a rotation matrix rather than in terms of a sequence of rotation angles.

EXPRESS specification:

*)
TYPE ypr_rotation = ARRAY[ypr_index(yaw):ypr_index(roll)] OF plane_angle_measure;
END_TYPE;
(*

4.3 ARM entity definitions

This subclause specifies the ARM entities for this module. Each ARM application entity is an atomic element that embodies a unique application concept and contains attributes specifying the data elements of the entity. The ARM entities and definitions are specified below.

4.3.1 Cylindrical_pair_value   EXPRESS-GMapping table

A Cylindrical_pair_value is a type of Pair_value. A Cylindrical_pair_value specifies the set of pair parameters for a Cylindrical_pair.

EXPRESS specification:

*)
ENTITY Cylindrical_pair_value
  SUBTYPE OF (Pair_value);
  SELF\Pair_value.applies_to_pair : Cylindrical_pair;
  actual_translation : length_measure;
  actual_rotation : plane_angle_measure;
END_ENTITY;
(*

Attribute definitions:

applies_to_pair: the Cylindrical_pair to which the Cylindrical_pair_value applies.

actual_translation: the translation value.

actual_rotation: the angle of rotation.

4.3.2 Gear_pair_value   EXPRESS-GMapping table

A Gear_pair_value is a type of Pair_value. A Gear_pair_value specifies the pair parameters for the Gear_pair.

NOTE    If the gear pair is part of a more complex gear mechanism, the gear pair values as defined here may not be the primary design targets. In the case of a planetary gear mechanism, for example, it is more important to know the rotation angles of the planetary gears with respect to an inertial coordinate system than the rotation angles between the planetary gears and the frames which support them. See [3] for a detailed description of this specific example.

For a given configuration of pairs within a mechanism, the more global motion parameters can be derived, in general, from the individual pair parameters and vice versa. This is not possible, however, generically without knowledge of the configuration. Therefore, the specification of functions which provide such derivations is left to an application protocol for which these derivations are required.

EXPRESS specification:

*)
ENTITY Gear_pair_value
  SUBTYPE OF (Pair_value);
  SELF\Pair_value.applies_to_pair : Gear_pair;
  actual_rotation_1 : plane_angle_measure;
DERIVE
  actual_rotation_2 : plane_angle_measure := - actual_rotation_1 * SELF\pair_value.applies_to_pair\ gear_pair.gear_ratio;
END_ENTITY;
(*

Attribute definitions:

applies_to_pair: the Gear_pair to which the Gear_pair_value applies.

actual_rotation_1: the value of the pair parameter of the first link.

actual_rotation_2: the value of the pair parameter of the second link.

4.3.3 Mechanism_state_representation   EXPRESS-GMapping table

A Mechanism_state_representation is a type of Representation that specifies a particular state of a Mechanism_representation by applying Pair_values for each Kinematic_pair of the underlying Mechanism_representation.

EXPRESS specification:

*)
ENTITY Mechanism_state_representation
  SUBTYPE OF (Representation);
  SELF\Representation.items : SET[1:?] OF Pair_value;
  represented_mechanism : Mechanism_representation;
DERIVE
  SELF\Representation.context_of_items : Geometric_coordinate_space := represented_mechanism.context_of_items;
END_ENTITY;
(*

Attribute definitions:

items: an inherited attribute that shall be of type Pair_value. There shall exist at least one Pair_value for the Mechanism_state_representation.

represented_mechanism: specifies the Mechanism_representation for which a particular state is represented.

context_of_items: an inherited attribute that shall be of type Geometric_coordinate_space.

4.3.4 Pair_value   EXPRESS-GMapping table

A Pair_value is a type of Detailed_geometric_model_element that specifies a configuration of the two links that join a Kinematic_pair. Each Pair_value is either a Sliding_surface_pair_value, a Rolling_surface_pair_value, a Revolute_pair_value, a Prismatic_pair_value, a Screw_pair_value, a Cylindrical_pair_value, a Spherical_pair_value, a Sliding_curve_pair_value, a Rolling_curve_pair_value, a Gear_pair_value, a Rack_and_pinion_pair_value, a Universal_pair_value, a Planar_pair_value, an Unconstrained_pair_value, a Point_on_surface_pair_value, or a Point_on_planar_curve_pair_value

EXPRESS specification:

*)
ENTITY Pair_value
  ABSTRACT SUPERTYPE OF (ONEOF (Sliding_surface_pair_value,
                                Rolling_surface_pair_value,
                                Revolute_pair_value,
                                Prismatic_pair_value,
                                Screw_pair_value,
                                Cylindrical_pair_value,
                                Spherical_pair_value,
                                Sliding_curve_pair_value,
                                Rolling_curve_pair_value,
                                Gear_pair_value,
                                Rack_and_pinion_pair_value,
                                Universal_pair_value,
                                Planar_pair_value,
                                Unconstrained_pair_value,
                                Point_on_surface_pair_value,
                                Point_on_planar_curve_pair_value))
  SUBTYPE OF (Detailed_geometric_model_element);
  applies_to_pair : Kinematic_pair;
END_ENTITY;
(*

Attribute definitions:

applies_to_pair: the Kinematic_pair to which the Pair_value applies.

4.3.5 Planar_pair_value   EXPRESS-GMapping table

A Planar_pair_value is a type of Pair_value. A Planar_pair_value specifies the set of pair parameters for the Planar_pair.

EXPRESS specification:

*)
ENTITY Planar_pair_value
  SUBTYPE OF (Pair_value);
  SELF\Pair_value.applies_to_pair : Planar_pair;
  actual_rotation : plane_angle_measure;
  actual_translation_x : length_measure;
  actual_translation_y : length_measure;
END_ENTITY;
(*

Attribute definitions:

applies_to_pair: the Planar_pair to which the Planar_pair_value applies.

actual_rotation: the value of the angle of rotation for a Planar_pair.

actual_translation_x: the value of translation in x-direction for a Planar_pair.

actual_translation_y: the value of translation in y-direction for a Planar_pair.

4.3.6 Point_on_planar_curve_pair_value   EXPRESS-GMapping table

A Point_on_planar_curve_pair_value is a type of Pair_value. A Point_on_planar_curve_pair_value specifies the pair parameters for the Point_on_planar_curve_pair.

EXPRESS specification:

*)
ENTITY Point_on_planar_curve_pair_value
  SUBTYPE OF (Pair_value);
  SELF\Pair_value.applies_to_pair : Point_on_planar_curve_pair;
  actual_point_on_curve : Point_on_curve;
  input_orientation : spatial_rotation;
WHERE
  WR1: SELF\pair_value.applies_to_pair\point_on_planar_curve_pair.pair_curve :=: actual_point_on_curve.supporting_curve;
END_ENTITY;
(*

Attribute definitions:

applies_to_pair: the Point_on_planar_curve_pair to which the Point_on_planar_curve_pair_value applies.

actual_point_on_curve: the positional value for the point on the curve.

input_orientation: the input specification of the rotational pair parameter values from which the actual orientation is derived. An input_orientation is either a ypr_rotation or a Rotation_about_direction.

Formal propositions:

WR1: The actual_point_on_curve shall be defined as a point on the pair_curve of the Point_on_planar_curve_pair referenced by applies_to_pair.

4.3.7 Point_on_surface_pair_value   EXPRESS-GMapping table

A Point_on_surface_pair_value is a type of Pair_value. A Point_on_surface_pair_value specifies the pair parameters for the Point_on_surface_pair.

EXPRESS specification:

*)
ENTITY Point_on_surface_pair_value
  SUBTYPE OF (Pair_value);
  SELF\Pair_value.applies_to_pair : Point_on_surface_pair;
  actual_point_on_surface : Point_on_surface;
  input_orientation : spatial_rotation;
WHERE
  WR1: SELF\pair_value.applies_to_pair\Point_on_surface_pair.pair_surface :=: actual_point_on_surface.supporting_surface;
END_ENTITY;
(*

Attribute definitions:

applies_to_pair: the Point_on_surface_pair to which the Point_on_surface_pair_value applies.

actual_point_on_surface: the positional value for the point on the surface.

input_orientation: the input specification of the rotational pair parameter values from which the actual orientation is derived. An input_orientation is either an ypr_rotation or a Rotation_about_direction.

Formal propositions:

WR1: The actual_point_on_surface shall be defined as a point on the pair_surface of the Point_on_surface_pair referenced by applies_to_pair.

4.3.8 Prismatic_pair_value   EXPRESS-GMapping table

A Prismatic_pair_value is a type of Pair_value. A Prismatic_pair_value is the value of the pair parameter for the Prismatic_pair.

EXPRESS specification:

*)
ENTITY Prismatic_pair_value
  SUBTYPE OF (Pair_value);
  SELF\Pair_value.applies_to_pair : Prismatic_pair;
  actual_translation : length_measure;
END_ENTITY;
(*

Attribute definitions:

applies_to_pair: the Prismatic_pair to which the Prismatic_pair_value applies.

actual_translation: the value of the pair parameter.

4.3.9 Rack_and_pinion_pair_value   EXPRESS-GMapping table

A Rack_and_pinion_pair_value is a type of Pair_value. A Rack_and_pinion_pair_value specifies the pair parameters for the Rack_and_pinion_pair.

EXPRESS specification:

*)
ENTITY Rack_and_pinion_pair_value
  SUBTYPE OF (Pair_value);
  SELF\Pair_value.applies_to_pair : Rack_and_pinion_pair;
  actual_displacement : length_measure;
DERIVE
  actual_rotation : plane_angle_measure := 0.0;
END_ENTITY;
(*

Attribute definitions:

applies_to_pair: the Rack_and_pinion_pair to which the Rack_and_pinion_pair_value applies.

actual_displacement: the value of the pair parameter for the rack.

actual_rotation: the resulting rotation of the pinion.

4.3.10 Revolute_pair_value   EXPRESS-GMapping table

A Revolute_pair_value is a type of Pair_value. A Revolute_pair_value specifies the value of the pair parameter for the Revolute_pair.

EXPRESS specification:

*)
ENTITY Revolute_pair_value
  SUBTYPE OF (Pair_value);
  SELF\Pair_value.applies_to_pair : Revolute_pair;
  actual_rotation : plane_angle_measure;
END_ENTITY;
(*

Attribute definitions:

applies_to_pair: the Revolute_pair to which the Revolute_pair_value applies.

actual_rotation: the value of the pair parameter.

4.3.11 Rolling_curve_pair_value   EXPRESS-GMapping table

A Rolling_curve_pair_value is a type of Pair_value. A Rolling_curve_pair_value specifies the pair parameter for the Rolling_curve_pair.

EXPRESS specification:

*)
ENTITY Rolling_curve_pair_value
  SUBTYPE OF (Pair_value);
  SELF\Pair_value.applies_to_pair : Rolling_curve_pair;
  actual_point_on_curve_1 : Point_on_curve;
WHERE
  WR1: SELF\pair_value.applies_to_pair\planar_curve_pair.curve_1 :=: actual_point_on_curve_1.supporting_curve;
END_ENTITY;
(*

Attribute definitions:

applies_to_pair: the Rolling_curve_pair to which the Rolling_curve_pair_value applies.

actual_point_on_curve_1: the contact point, defined in the parameter space of the curve on the first link.

Formal propositions:

WR1: The actual_point_on_curve_1 shall be defined as a point on curve_1 of the Planar_curve_pair referenced by applies_to_pair.

4.3.12 Rolling_surface_pair_value   EXPRESS-GMapping table

A Rolling_surface_pair_value is a type of Pair_value. A Rolling_surface_pair_value specifies the set of pair parameters for the Rolling_surface_pair.

EXPRESS specification:

*)
ENTITY Rolling_surface_pair_value
  SUBTYPE OF (Pair_value);
  SELF\Pair_value.applies_to_pair : Rolling_surface_pair;
  actual_point_on_surface : Point_on_surface;
  actual_rotation : plane_angle_measure;
WHERE
  WR1: SELF\pair_value.applies_to_pair\surface_pair.surface_1 :=: actual_point_on_surface.supporting_surface;
END_ENTITY;
(*

Attribute definitions:

applies_to_pair: the Rolling_surface_pair to which the Rolling_surface_pair_value applies.

actual_point_on_surface: the contact point of the contact surface (surface_1) of the first link.

actual_rotation: the angle required to rotate the xcp-direction of the first link surface around the zc-direction of that surface until it coincides with the xc-direction of the second link surface.

Formal propositions:

WR1: The actual_point_on_surface shall be defined as a point on surface_1 of the Surface_pair referenced by applies_to_pair.

4.3.13 Rotation_about_direction   EXPRESS-GMapping table

A Rotation_about_direction is a type of Detailed_geometric_model_element that specifies a rotation in Cartesian coordinate space R3. The axis of rotation passes the origin of the related coordinate system; its direction is given explicitely as direction_of_axis. Furthermore, the amount of rotation is specified by rotation_angle which may have any finite value; i.e., its absolute value in radians is not restricted to be less than π. A positive value of rotation_angle indicates a counter-clockwise rotation when looking in the negative direction with respect to the direction_of_axis.

EXPRESS specification:

*)
ENTITY Rotation_about_direction
  SUBTYPE OF (Detailed_geometric_model_element);
  direction_of_axis : Direction;
  rotation_angle : plane_angle_measure;
WHERE
  WR1: SIZEOF (direction_of_axis.direction_ratios) = 3;
END_ENTITY;
(*

Attribute definitions:

direction_of_axis: the three-dimensional direction of the axis of rotation.

rotation_angle: the angle of rotation about the axis of rotation.

Formal propositions:

WR1: The direction_of_axis shall be a three-dimensional direction.

4.3.14 Screw_pair_value   EXPRESS-GMapping table

A Screw_pair_value is a type of Pair_value. A Screw_pair_value specifies the value of the pair parameter of the Screw_pair.

EXPRESS specification:

*)
ENTITY Screw_pair_value
  SUBTYPE OF (Pair_value);
  SELF\Pair_value.applies_to_pair : Screw_pair;
  actual_rotation : plane_angle_measure;
END_ENTITY;
(*

Attribute definitions:

applies_to_pair: the Screw_pair to which the Screw_pair_value applies.

actual_rotation: the rotation angle of the Screw_pair.

4.3.15 Sliding_curve_pair_value   EXPRESS-GMapping table

A Sliding_curve_pair_value is a type of Pair_value. A Sliding_curve_pair_value specifies the pair parameters for the Sliding_curve_pair.

EXPRESS specification:

*)
ENTITY Sliding_curve_pair_value
  SUBTYPE OF (Pair_value);
  SELF\Pair_value.applies_to_pair : Sliding_curve_pair;
  actual_point_on_curve_1 : Point_on_curve;
  actual_point_on_curve_2 : Point_on_curve;
WHERE
  WR1: SELF\pair_value.applies_to_pair\planar_curve_pair.curve_1 :=: actual_point_on_curve_1.supporting_curve;
  WR2: SELF\pair_value.applies_to_pair\planar_curve_pair.curve_2 :=: actual_point_on_curve_2.supporting_curve;
END_ENTITY;
(*

Attribute definitions:

applies_to_pair: the Sliding_curve_pair to which the Sliding_curve_pair_value applies.

actual_point_on_curve_1: the contact point, defined in the parameter space of the curve on the first link.

actual_point_on_curve_2: the contact point, defined in the parameter space of the curve on the second link.

Formal propositions:

WR1: The actual_point_on_curve_1 shall be defined as a point on curve_1 of the Planar_curve_pair referenced by applies_to_pair.

WR2: The actual_point_on_curve_2 shall be defined as a point on curve_2 of the Planar_curve_pair referenced by applies_to_pair.

4.3.16 Sliding_surface_pair_value   EXPRESS-GMapping table

A Sliding_surface_pair_value is a type of Pair_value. A Sliding_surface_pair_value specifies the set of pair parameters for the Sliding_surface_pair.

EXPRESS specification:

*)
ENTITY Sliding_surface_pair_value
  SUBTYPE OF (Pair_value);
  SELF\Pair_value.applies_to_pair : Sliding_surface_pair;
  actual_point_on_surface_1 : Point_on_surface;
  actual_point_on_surface_2 : Point_on_surface;
  actual_rotation : plane_angle_measure;
WHERE
  WR1: SELF\pair_value.applies_to_pair\surface_pair.surface_1 :=: actual_point_on_surface_1.supporting_surface;
  WR2: SELF\pair_value.applies_to_pair\surface_pair.surface_2 :=: actual_point_on_surface_2.supporting_surface;
END_ENTITY;
(*

Attribute definitions:

applies_to_pair: the Sliding_surface_pair to which the Sliding_surface_pair_value applies.

actual_point_on_surface_1: the contact point of the contact surface (surface_1) of the first link.

actual_point_on_surface_2: the contact point of the contact surface (surface_2) of the second link.

actual_rotation: the angle required to rotate the xcp-direction of the first link surface around the zc-direction of that surface until it coincides with the xc-direction of the second link surface.

Formal propositions:

WR1: The actual_point_on_surface_1 shall be defined as a point on surface_1 of the Surface_pair referenced by applies_to_pair.

WR2: The actual_point_on_surface_2 shall be defined as a point on surface_2 of the Surface_pair referenced by applies_to_pair.

4.3.17 Spherical_pair_value   EXPRESS-GMapping table

A Spherical_pair_value is a type of Pair_value. A Spherical_pair_value specifies the set of pair parameters for a Spherical_pair.

EXPRESS specification:

*)
ENTITY Spherical_pair_value
  SUBTYPE OF (Pair_value);
  SELF\Pair_value.applies_to_pair : Spherical_pair;
  input_orientation : spatial_rotation;
END_ENTITY;
(*

Attribute definitions:

applies_to_pair: the Spherical_pair to which the Spherical_pair_value applies.

input_orientation: the input specification of the pair parameter values from which the actual orientation is derived. An input_orientation is either an ypr_rotation or a Rotation_about_direction.

4.3.18 Unconstrained_pair_value   EXPRESS-GMapping table

An Unconstrained_pair_value is a type of Pair_value An Unconstrained_pair_value specifies the pair parameters for an Unconstrained_pair.

EXPRESS specification:

*)
ENTITY Unconstrained_pair_value
  SUBTYPE OF (Pair_value);
  SELF\Pair_value.applies_to_pair : Unconstrained_pair;
  actual_placement : Axis_placement_3d;
END_ENTITY;
(*

Attribute definitions:

applies_to_pair: the Unconstrained_pair to which the Unconstrained_pair_value applies.

actual_placement: the placement of the second pair frame with respect to the first pair frame for the Unconstrained_pair.

4.3.19 Universal_pair_value   EXPRESS-GMapping table

A Universal_pair_value is a type of Pair_value. A Universal_pair_value specifies the set of pair parameters for a Universal_pair.

EXPRESS specification:

*)
ENTITY Universal_pair_value
  SUBTYPE OF (Pair_value);
  SELF\Pair_value.applies_to_pair : Universal_pair;
  first_rotation_angle : plane_angle_measure;
  second_rotation_angle : plane_angle_measure;
END_ENTITY;
(*

Attribute definitions:

applies_to_pair: the Universal_pair to which the Universal_pair_value applies.

first_rotation_angle: the angle of rotation around the first axis.

second_rotation_angle: the angle of rotation around the second axis.

4.4 ARM subtype constraint definition

This subclause specifies the ARM subtype constraint for this module. The subtype constraint places a constraint on the possible super-type / subtype instantiations. The ARM subtype constraint and definition is specified below.

4.4.1 kss_geometric_representation_item_subtypes   EXPRESS-GMapping table

The kss_geometric_representation_item_subtypes constraint specifies a constraint that applies to instances of Detailed_geometric_model_element and enforces the rule that its subtypes Rotation_about_direction and Su_parameters are exclusive.

EXPRESS specification:

*)
SUBTYPE_CONSTRAINT kss_geometric_representation_item_subtypes FOR Detailed_geometric_model_element;
  ONEOF (Rotation_about_direction,
         Su_parameters);
END_SUBTYPE_CONSTRAINT;
(*

4.5 ARM function definition

This subclause specifies the ARM function for this module. The ARM function and definition is specified below.

4.5.1 ypr_index

The ypr_index function establishes an ordered sequence of angles of rotation for a linear transformation. The function returns 1 if the angle of rotation is of type yaw. The function returns 2 if the angle of rotation is of type pitch. The function returns 3 if the angle of rotation is of type roll. The type of the function is INTEGER.

EXPRESS specification:

*)
FUNCTION ypr_index (ypr : ypr_enumeration) : INTEGER; 
CASE ypr OF
    yaw    : RETURN (1);
    pitch  : RETURN (2);
    roll   : RETURN (3);
  END_CASE;
  RETURN (?);
END_FUNCTION;
(*

Argument definitions:

ypr: one axis of rotation as specified by the ypr_enumeration.



*)
END_SCHEMA;  -- Kinematic_state_arm
(*

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