ISO/TS 10303-1797:2018-11 Kinematic structure


Application module: Kinematic structure	ISO/TS 10303-1797:2018-11(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 ARMs
4.2 ARM type definitions
4.3 ARM entity definitions
4.4 ARM subtype constraint definitions
4.5 ARM function definitions
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
D MIM EXPRESS-G
E Computer interpretable listings
F Change history
Bibliography
Index


         (*
ISO/TC 184/SC 4/WG 12 N9364 - ISO/TS 10303-1797 Kinematic structure - EXPRESS ARM
Supersedes 
         ISO/TC 184/SC 4/WG 12 N7909
*)



SCHEMA Kinematic_structure_arm;


         USE FROM
         Kinematic_topology_arm;
            -- ISO/TS 10303-1799


         USE FROM
         Basic_curve_arm;
            -- ISO/TS 10303-1651


         USE FROM
         Assembly_structure_arm;
            -- ISO/TS 10303-1026


         USE FROM
         Geometric_model_relationship_arm;
            -- ISO/TS 10303-1403


         USE FROM
         Composite_surface_arm;
            -- ISO/TS 10303-1525


         USE FROM
         Shape_property_assignment_arm;
            -- ISO/TS 10303-1032


         REFERENCE FROM 
         Kinematic_topology_arm   -- ISO/TS 10303-1799
  (get_kinematic_joints_from_oriented_joints,

           
         get_kinematic_joints_from_kinematic_loops);


         REFERENCE FROM 
         Foundation_representation_arm   -- ISO/TS 10303-1006
  (using_representations);


TYPE actuated_direction =
         
         ENUMERATION
         
         OF
         

            
         (bidirectional,
    positive_only,
    negative_only,
    not_actuated);

         END_TYPE;


TYPE kinematic_link_representation_items =
         
         
         SELECT

            (Curve, 
    Cartesian_point, 
    rigid_placement, 
    Surface);

         END_TYPE;


TYPE ks_additional_application_domain_enumeration =
         
         ENUMERATION
         
         BASED_ON 
         additional_application_domain_enumeration
         WITH 
         

            
         (kinematic_mechanism);

         END_TYPE;


TYPE ks_geometric_representation_select =
         
         EXTENSIBLE
         
         GENERIC_ENTITY
         
         
         SELECT
         BASED_ON
         geometric_representation_select
         WITH 
         

            (Kinematic_link_representation);

         END_TYPE;


TYPE ks_property_assignment_select =
         
         
         SELECT
         BASED_ON
         property_assignment_select
         WITH 
         

            (Assembly_component_relationship);

         END_TYPE;


TYPE rigid_placement =
         
         
         SELECT

            (Axis_placement_3d, 
    Su_parameters);

         END_TYPE;


ENTITY Actuated_kinematic_pair

           SUBTYPE OF (Kinematic_pair);

           t_x : 
         OPTIONAL 
         actuated_direction;

           t_y : 
         OPTIONAL 
         actuated_direction;

           t_z : 
         OPTIONAL 
         actuated_direction;

           r_x : 
         OPTIONAL 
         actuated_direction;

           r_y : 
         OPTIONAL 
         actuated_direction;

           r_z : 
         OPTIONAL 
         actuated_direction;

         
         END_ENTITY;


ENTITY Context_dependent_kinematic_link_representation;

           representation_relation : Kinematic_link_representation_association;

           represented_product_relation : Product_definition_relationship_kinematics;

         
         END_ENTITY;


ENTITY Cylindrical_pair

           SUBTYPE OF (Low_order_kinematic_pair);
DERIVE

           SELF\Low_order_kinematic_pair.t_x : BOOLEAN := FALSE;

           SELF\Low_order_kinematic_pair.t_y : BOOLEAN := FALSE;

           SELF\Low_order_kinematic_pair.t_z : BOOLEAN := TRUE;

           SELF\Low_order_kinematic_pair.r_x : BOOLEAN := FALSE;

           SELF\Low_order_kinematic_pair.r_y : BOOLEAN := FALSE;

           SELF\Low_order_kinematic_pair.r_z : BOOLEAN := TRUE;

         
         END_ENTITY;


ENTITY Cylindrical_pair_with_range

           SUBTYPE OF (Cylindrical_pair);

           lower_limit_actual_translation : 
         OPTIONAL 
         length_measure;

           upper_limit_actual_translation : 
         OPTIONAL 
         length_measure;

           lower_limit_actual_rotation : 
         OPTIONAL 
         plane_angle_measure;

           upper_limit_actual_rotation : 
         OPTIONAL 
         plane_angle_measure;
WHERE

           WR1: (NOT EXISTS(lower_limit_actual_translation)
            OR
            NOT EXISTS(upper_limit_actual_translation))
            XOR
            (lower_limit_actual_translation < upper_limit_actual_translation);

           WR2: (NOT EXISTS(lower_limit_actual_rotation)
            OR
            NOT EXISTS(upper_limit_actual_rotation))
            XOR
            (lower_limit_actual_rotation < upper_limit_actual_rotation);

         
         END_ENTITY;


ENTITY Fully_constrained_pair

           SUBTYPE OF (Low_order_kinematic_pair);
DERIVE

           SELF\Low_order_kinematic_pair.t_x : BOOLEAN := FALSE;

           SELF\Low_order_kinematic_pair.t_y : BOOLEAN := FALSE;

           SELF\Low_order_kinematic_pair.t_z : BOOLEAN := FALSE;

           SELF\Low_order_kinematic_pair.r_x : BOOLEAN := FALSE;

           SELF\Low_order_kinematic_pair.r_y : BOOLEAN := FALSE;

           SELF\Low_order_kinematic_pair.r_z : BOOLEAN := FALSE;

         
         END_ENTITY;


ENTITY Gear_pair

           SUBTYPE OF (Low_order_kinematic_pair_with_motion_coupling);

           radius_first_link : length_measure;

           radius_second_link : length_measure;

           bevel : plane_angle_measure;

           helical_angle : plane_angle_measure;

           gear_ratio : REAL;
WHERE

           WR1: SIZEOF( QUERY(lr <* SELF\Kinematic_pair.associated_link_representations_1 | 
            NOT('KINEMATIC_STRUCTURE_ARM.RIGID_LINK_REPRESENTATION' IN TYPEOF(lr)))) = 0;

         
         END_ENTITY;


ENTITY Gear_pair_with_range

           SUBTYPE OF (Gear_pair);

           lower_limit_actual_rotation_1 : 
         OPTIONAL 
         plane_angle_measure;

           upper_limit_actual_rotation_1 : 
         OPTIONAL 
         plane_angle_measure;
WHERE

           WR1: (NOT EXISTS(lower_limit_actual_rotation_1)
            OR
            NOT EXISTS(upper_limit_actual_rotation_1))
            XOR
            (lower_limit_actual_rotation_1 < upper_limit_actual_rotation_1);

         
         END_ENTITY;


ENTITY High_order_kinematic_pair

           ABSTRACT SUPERTYPE
         
         OF (ONEOF (Linear_flexible_and_planar_curve_pair,
                                Point_on_surface_pair,
                                Point_on_planar_curve_pair,
                                Planar_curve_pair,
                                Surface_pair))

           SUBTYPE OF (Kinematic_pair);
WHERE

           WR1: SIZEOF( QUERY(lr <* SELF\Kinematic_pair.associated_link_representations_2 | 
            NOT('KINEMATIC_STRUCTURE_ARM.RIGID_LINK_REPRESENTATION' IN TYPEOF(lr)))) = 0;

         
         END_ENTITY;


ENTITY Homokinetic_pair

           SUBTYPE OF (Universal_pair);
WHERE

           WR1: NOT EXISTS(SELF.input_skew_angle);

         
         END_ENTITY;


ENTITY Kinematic_link_representation

           ABSTRACT SUPERTYPE
         
         OF (ONEOF (Linear_flexible_link_representation,
                                Rigid_link_representation))

           SUBTYPE OF (Representation);

           SELF\Representation.context_of_items : Geometric_coordinate_space;

           SELF\Representation.items : SET[1:?] OF kinematic_link_representation_items;

           represented_link : Kinematic_link;
INVERSE

           associated_shape_representation : SET[0:1] OF Kinematic_link_representation_association FOR rep_1;

         
         END_ENTITY;


ENTITY Kinematic_link_representation_association

           SUBTYPE OF (Representation_relationship);

           SELF\Representation_relationship.rep_1 : Kinematic_link_representation;

           SELF\Representation_relationship.rep_2 : Geometric_model;
WHERE

           WR1: (SELF\Representation_relationship.rep_2.context_of_items :=:
            SELF\Representation_relationship.rep_1.context_of_items) OR
            ('CONTEXTUAL_SHAPE_POSITIONING_ARM.GEOMETRIC_MODEL_RELATIONSHIP_WITH_TRANSFORMATION' IN TYPEOF(SELF));

         
         END_ENTITY;


ENTITY Kinematic_pair

           ABSTRACT SUPERTYPE
         
         OF (ONEOF (High_order_kinematic_pair,
                                Low_order_kinematic_pair_with_motion_coupling,
                                Low_order_kinematic_pair)
                        ANDOR Actuated_kinematic_pair)

           SUBTYPE OF (Detailed_geometric_model_element);

           joint : Kinematic_joint;

           transform_item_1 : rigid_placement;

           transform_item_2 : rigid_placement;
DERIVE

           associated_link_representations_1 : SET[1:?] OF Kinematic_link_representation := sort_link_associations(link_representation_associations, TRUE);

           associated_link_representations_2 : SET[1:?] OF Kinematic_link_representation := sort_link_associations(link_representation_associations, FALSE);
INVERSE

           link_representation_associations : SET[1:?] OF Pair_representation_relationship FOR transformation_operator;

         
         END_ENTITY;


ENTITY Kinematic_property_mechanism_representation

           SUBTYPE OF (Kinematic_property_definition_representation);

           SELF\Property_definition_representation.used_representation : Mechanism_representation;

           base : Kinematic_link_representation;
WHERE

           WR1: SIZEOF( QUERY( i <* used_representation.items |
            (base :=: i\Representation_relationship.rep_1) OR
            (base :=: i\Representation_relationship.rep_2))) > 0;

         
         END_ENTITY;


ENTITY Linear_flexible_and_pinion_pair

           SUBTYPE OF (Low_order_kinematic_pair_with_motion_coupling);

           pinion_radius : length_measure;
WHERE

           WR1: SIZEOF( QUERY(lr <* SELF\Kinematic_pair.associated_link_representations_1 | 
            NOT('KINEMATIC_STRUCTURE_ARM.LINEAR_FLEXIBLE_LINK_REPRESENTATION' IN TYPEOF(lr)))) = 0;

         
         END_ENTITY;


ENTITY Linear_flexible_and_planar_curve_pair

           SUBTYPE OF (High_order_kinematic_pair);

           pair_curve : Curve;

           orientation : BOOLEAN;
WHERE

           WR1: SIZEOF( QUERY(r <* SELF\Kinematic_pair.associated_link_representations_1 | NOT(pair_curve IN r.items))) = 0;

           WR2: SIZEOF( QUERY(lr <* SELF\Kinematic_pair.associated_link_representations_1 | 
            NOT('KINEMATIC_STRUCTURE_ARM.LINEAR_FLEXIBLE_LINK_REPRESENTATION' IN TYPEOF(lr)))) = 0;

         
         END_ENTITY;


ENTITY Linear_flexible_link_representation

           SUBTYPE OF (Kinematic_link_representation);

         
         END_ENTITY;


ENTITY Low_order_kinematic_pair

           SUPERTYPE OF 
         (ONEOF (Revolute_pair,
                       Cylindrical_pair,
                       Spherical_pair,
                       Spherical_pair_with_pin,
                       Planar_pair,
                       Unconstrained_pair,
                       Fully_constrained_pair,
                       Prismatic_pair,
                       Universal_pair))

           SUBTYPE OF (Kinematic_pair);

           t_x : BOOLEAN;

           t_y : BOOLEAN;

           t_z : BOOLEAN;

           r_x : BOOLEAN;

           r_y : BOOLEAN;

           r_z : BOOLEAN;
WHERE

           WR1: SIZEOF( QUERY(lr <* SELF\Kinematic_pair.associated_link_representations_1 | 
            NOT('KINEMATIC_STRUCTURE_ARM.RIGID_LINK_REPRESENTATION' IN TYPEOF(lr)))) = 0;

           WR2: SIZEOF( QUERY(lr <* SELF\Kinematic_pair.associated_link_representations_2 | 
            NOT('KINEMATIC_STRUCTURE_ARM.RIGID_LINK_REPRESENTATION' IN TYPEOF(lr)))) = 0;

         
         END_ENTITY;


ENTITY Low_order_kinematic_pair_with_motion_coupling

           ABSTRACT SUPERTYPE
         
         OF (ONEOF (Gear_pair,
                                Linear_flexible_and_pinion_pair,
                                Rack_and_pinion_pair,
                                Screw_pair))

           SUBTYPE OF (Kinematic_pair);
WHERE

           WR1: SIZEOF( QUERY(lr <* SELF\Kinematic_pair.associated_link_representations_2 | 
            NOT('KINEMATIC_STRUCTURE_ARM.RIGID_LINK_REPRESENTATION' IN TYPEOF(lr)))) = 0;

         
         END_ENTITY;


ENTITY Mechanism_representation

           SUBTYPE OF (Representation);

           SELF\Representation.context_of_items : Geometric_coordinate_space;

           SELF\Representation.items : SET[1:?] OF Pair_representation_relationship;

           represented_topology : kinematic_topology_representation_select;
DERIVE

           represented_joints : SET[1:?] OF Kinematic_joint := collect_joints(items);
WHERE

           WR1: (('KINEMATIC_TOPOLOGY_ARM.KINEMATIC_TOPOLOGY_STRUCTURE' IN TYPEOF(represented_topology))
            AND (represented_joints :=: represented_topology.items)) OR
            (('KINEMATIC_TOPOLOGY_ARM.KINEMATIC_TOPOLOGY_DIRECTED_STRUCTURE' IN TYPEOF(represented_topology))
            AND (represented_joints :=: get_kinematic_joints_from_oriented_joints(represented_topology.items))) OR
            (('KINEMATIC_TOPOLOGY_ARM.KINEMATIC_TOPOLOGY_NETWORK_STRUCTURE' IN TYPEOF(represented_topology))
            AND (represented_joints :=: get_kinematic_joints_from_kinematic_loops(represented_topology.items)));

         
         END_ENTITY;


ENTITY Pair_representation_relationship

           SUBTYPE OF (Detailed_geometric_model_element, Geometric_model_relationship);

           SELF\Representation_relationship.rep_1 : Kinematic_link_representation;

           SELF\Representation_relationship.rep_2 : Kinematic_link_representation;

           transformation_operator : Kinematic_pair;
WHERE

           WR1: transformation_operator.transform_item_1 IN rep_1.items;

           WR2: transformation_operator.transform_item_2 IN rep_2.items;

           WR3: rep_1\kinematic_link_representation.represented_link = transformation_operator\kinematic_pair.joint.edge_start;

           WR4: rep_2\kinematic_link_representation.represented_link = transformation_operator\kinematic_pair.joint.edge_end;

         
         END_ENTITY;


ENTITY Planar_curve_pair

           SUPERTYPE OF 
         (ONEOF (Sliding_curve_pair,
                       Rolling_curve_pair)
               ANDOR Planar_curve_pair_range)

           SUBTYPE OF (High_order_kinematic_pair);

           curve_1 : Curve;

           curve_2 : Curve;

           orientation : BOOLEAN;
WHERE

           WR1: SIZEOF( QUERY(r <* SELF\Kinematic_pair.associated_link_representations_1 | NOT(curve_1 IN r.items))) = 0;

           WR2: SIZEOF( QUERY(r <* SELF\Kinematic_pair.associated_link_representations_2 | NOT(curve_2 IN r.items))) = 0;

           WR3: SIZEOF( QUERY(lr <* SELF\Kinematic_pair.associated_link_representations_1 | 
            NOT('KINEMATIC_STRUCTURE_ARM.RIGID_LINK_REPRESENTATION' IN TYPEOF(lr)))) = 0;

         
         END_ENTITY;


ENTITY Planar_curve_pair_range

           SUBTYPE OF (Planar_curve_pair);

           range_on_curve_1 : Trimmed_curve;

           range_on_curve_2 : Trimmed_curve;
WHERE

           WR1: SELF\Planar_curve_pair.curve_1 :=: range_on_curve_1.basis_curve;

           WR2: SELF\Planar_curve_pair.curve_2 :=: range_on_curve_2.basis_curve;

           WR3: SIZEOF( QUERY(r <* SELF\Kinematic_pair.associated_link_representations_1 | NOT(range_on_curve_1 IN r.items))) = 0;

           WR4: SIZEOF( QUERY(r <* SELF\Kinematic_pair.associated_link_representations_2 | NOT(range_on_curve_2 IN r.items))) = 0;

         
         END_ENTITY;


ENTITY Planar_pair

           SUBTYPE OF (Low_order_kinematic_pair);
DERIVE

           SELF\Low_order_kinematic_pair.t_x : BOOLEAN := TRUE;

           SELF\Low_order_kinematic_pair.t_y : BOOLEAN := TRUE;

           SELF\Low_order_kinematic_pair.t_z : BOOLEAN := FALSE;

           SELF\Low_order_kinematic_pair.r_x : BOOLEAN := FALSE;

           SELF\Low_order_kinematic_pair.r_y : BOOLEAN := FALSE;

           SELF\Low_order_kinematic_pair.r_z : BOOLEAN := TRUE;

         
         END_ENTITY;


ENTITY Planar_pair_with_range

           SUBTYPE OF (Planar_pair);

           lower_limit_actual_rotation : 
         OPTIONAL 
         plane_angle_measure;

           upper_limit_actual_rotation : 
         OPTIONAL 
         plane_angle_measure;

           lower_limit_actual_translation_x : 
         OPTIONAL 
         length_measure;

           upper_limit_actual_translation_x : 
         OPTIONAL 
         length_measure;

           lower_limit_actual_translation_y : 
         OPTIONAL 
         length_measure;

           upper_limit_actual_translation_y : 
         OPTIONAL 
         length_measure;
WHERE

           WR1: (NOT EXISTS(lower_limit_actual_rotation)
            OR
            NOT EXISTS(upper_limit_actual_rotation))
            XOR
            (lower_limit_actual_rotation < upper_limit_actual_rotation);

           WR2: (NOT EXISTS(lower_limit_actual_translation_x)
            OR
            NOT EXISTS(upper_limit_actual_translation_x))
            XOR
            (lower_limit_actual_translation_x < upper_limit_actual_translation_x);

           WR3: (NOT EXISTS(lower_limit_actual_translation_y)
            OR
            NOT EXISTS(upper_limit_actual_translation_y))
            XOR
            (lower_limit_actual_translation_y < upper_limit_actual_translation_y);

         
         END_ENTITY;


ENTITY Point_on_planar_curve_pair

           SUBTYPE OF (High_order_kinematic_pair);

           pair_curve : Curve;

           orientation : BOOLEAN;
WHERE

           WR1: SIZEOF( QUERY(r <* SELF\Kinematic_pair.associated_link_representations_1 | NOT(pair_curve IN r.items))) = 0;

           WR2: SIZEOF( QUERY(lr <* SELF\Kinematic_pair.associated_link_representations_1 | 
            NOT('KINEMATIC_STRUCTURE_ARM.RIGID_LINK_REPRESENTATION' IN TYPEOF(lr)))) = 0;

         
         END_ENTITY;


ENTITY Point_on_planar_curve_pair_with_range

           SUBTYPE OF (Point_on_planar_curve_pair);

           range_on_pair_curve : Trimmed_curve;

           lower_limit_yaw : 
         OPTIONAL 
         plane_angle_measure;

           upper_limit_yaw : 
         OPTIONAL 
         plane_angle_measure;

           lower_limit_pitch : 
         OPTIONAL 
         plane_angle_measure;

           upper_limit_pitch : 
         OPTIONAL 
         plane_angle_measure;

           lower_limit_roll : 
         OPTIONAL 
         plane_angle_measure;

           upper_limit_roll : 
         OPTIONAL 
         plane_angle_measure;
WHERE

           WR1: (NOT EXISTS(lower_limit_pitch)
            OR
            NOT EXISTS(upper_limit_pitch))
            XOR
            (lower_limit_pitch < upper_limit_pitch);

           WR2: (NOT EXISTS(lower_limit_yaw)
            OR
            NOT EXISTS(upper_limit_yaw))
            XOR
            (lower_limit_yaw < upper_limit_yaw);

           WR3: (NOT EXISTS(lower_limit_roll)
            OR
            NOT EXISTS(upper_limit_roll))
            XOR
            (lower_limit_roll < upper_limit_roll);

           WR4: SIZEOF( QUERY(r <* SELF\Kinematic_pair.associated_link_representations_1 | NOT(range_on_pair_curve IN r.items))) = 0;

         
         END_ENTITY;


ENTITY Point_on_surface_pair

           SUBTYPE OF (High_order_kinematic_pair);

           pair_surface : Surface;
WHERE

           WR1: SIZEOF( QUERY(r <* SELF\Kinematic_pair.associated_link_representations_1 | NOT(pair_surface IN r.items))) = 0;

           WR2: SIZEOF( QUERY(lr <* SELF\Kinematic_pair.associated_link_representations_1 | 
            NOT('KINEMATIC_STRUCTURE_ARM.RIGID_LINK_REPRESENTATION' IN TYPEOF(lr)))) = 0;

         
         END_ENTITY;


ENTITY Point_on_surface_pair_with_range

           SUBTYPE OF (Point_on_surface_pair);

           range_on_pair_surface : Trimmed_surface;

           lower_limit_yaw : 
         OPTIONAL 
         plane_angle_measure;

           upper_limit_yaw : 
         OPTIONAL 
         plane_angle_measure;

           lower_limit_pitch : 
         OPTIONAL 
         plane_angle_measure;

           upper_limit_pitch : 
         OPTIONAL 
         plane_angle_measure;

           lower_limit_roll : 
         OPTIONAL 
         plane_angle_measure;

           upper_limit_roll : 
         OPTIONAL 
         plane_angle_measure;
WHERE

           WR1: (NOT EXISTS(lower_limit_pitch)
            OR
            NOT EXISTS(upper_limit_pitch))
            XOR
            (lower_limit_pitch < upper_limit_pitch);

           WR2: (NOT EXISTS(lower_limit_yaw)
            OR
            NOT EXISTS(upper_limit_yaw))
            XOR
            (lower_limit_yaw < upper_limit_yaw);

           WR3: (NOT EXISTS(lower_limit_roll)
            OR
            NOT EXISTS(upper_limit_roll))
            XOR
            (lower_limit_roll < upper_limit_roll);

           WR4: SIZEOF( QUERY(r <* SELF\Kinematic_pair.associated_link_representations_1 | NOT(range_on_pair_surface IN r.items))) =
            0;

         
         END_ENTITY;


ENTITY Prismatic_pair

           SUBTYPE OF (Low_order_kinematic_pair);
DERIVE

           SELF\Low_order_kinematic_pair.t_x : BOOLEAN := TRUE;

           SELF\Low_order_kinematic_pair.t_y : BOOLEAN := FALSE;

           SELF\Low_order_kinematic_pair.t_z : BOOLEAN := FALSE;

           SELF\Low_order_kinematic_pair.r_x : BOOLEAN := FALSE;

           SELF\Low_order_kinematic_pair.r_y : BOOLEAN := FALSE;

           SELF\Low_order_kinematic_pair.r_z : BOOLEAN := FALSE;

         
         END_ENTITY;


ENTITY Prismatic_pair_with_range

           SUBTYPE OF (Prismatic_pair);

           lower_limit_actual_translation : 
         OPTIONAL 
         length_measure;

           upper_limit_actual_translation : 
         OPTIONAL 
         length_measure;
WHERE

           WR1: (NOT EXISTS(lower_limit_actual_translation)
            OR
            NOT EXISTS(upper_limit_actual_translation))
            XOR
            (lower_limit_actual_translation < upper_limit_actual_translation);

         
         END_ENTITY;


ENTITY Product_definition_relationship_kinematics

           SUBTYPE OF (Assigned_property);

           SELF\Assigned_property.described_element : Assembly_component_relationship;
UNIQUE

           UR1: described_element;

         
         END_ENTITY;


ENTITY Rack_and_pinion_pair

           SUBTYPE OF (Low_order_kinematic_pair_with_motion_coupling);

           pinion_radius : length_measure;
WHERE

           WR1: SIZEOF( QUERY(lr <* SELF\Kinematic_pair.associated_link_representations_1 | 
            NOT('KINEMATIC_STRUCTURE_ARM.RIGID_LINK_REPRESENTATION' IN TYPEOF(lr)))) = 0;

         
         END_ENTITY;


ENTITY Rack_and_pinion_pair_with_range

           SUBTYPE OF (Rack_and_pinion_pair);

           lower_limit_rack_displacement : 
         OPTIONAL 
         length_measure;

           upper_limit_rack_displacement : 
         OPTIONAL 
         length_measure;
WHERE

           WR1: (NOT EXISTS(lower_limit_rack_displacement)
            OR
            NOT EXISTS(upper_limit_rack_displacement))
            XOR
            (lower_limit_rack_displacement < upper_limit_rack_displacement);

         
         END_ENTITY;


ENTITY Revolute_pair

           SUBTYPE OF (Low_order_kinematic_pair);
DERIVE

           SELF\Low_order_kinematic_pair.t_x : BOOLEAN := FALSE;

           SELF\Low_order_kinematic_pair.t_y : BOOLEAN := FALSE;

           SELF\Low_order_kinematic_pair.t_z : BOOLEAN := FALSE;

           SELF\Low_order_kinematic_pair.r_x : BOOLEAN := FALSE;

           SELF\Low_order_kinematic_pair.r_y : BOOLEAN := FALSE;

           SELF\Low_order_kinematic_pair.r_z : BOOLEAN := TRUE;

         
         END_ENTITY;


ENTITY Revolute_pair_with_range

           SUBTYPE OF (Revolute_pair);

           lower_limit_actual_rotation : 
         OPTIONAL 
         plane_angle_measure;

           upper_limit_actual_rotation : 
         OPTIONAL 
         plane_angle_measure;
WHERE

           WR1: (NOT EXISTS(lower_limit_actual_rotation)
            OR
            NOT EXISTS(upper_limit_actual_rotation))
            XOR
            (lower_limit_actual_rotation < upper_limit_actual_rotation);

         
         END_ENTITY;


ENTITY Rigid_link_representation

           SUBTYPE OF (Kinematic_link_representation);

         
         END_ENTITY;


ENTITY Rolling_curve_pair

           SUBTYPE OF (Planar_curve_pair);

         
         END_ENTITY;


ENTITY Rolling_surface_pair

           SUBTYPE OF (Surface_pair);

         
         END_ENTITY;


ENTITY Screw_pair

           SUBTYPE OF (Low_order_kinematic_pair_with_motion_coupling);

           pitch : length_measure;
WHERE

           WR1: SIZEOF( QUERY(lr <* SELF\Kinematic_pair.associated_link_representations_1 | 
            NOT('KINEMATIC_STRUCTURE_ARM.RIGID_LINK_REPRESENTATION' IN TYPEOF(lr)))) = 0;

         
         END_ENTITY;


ENTITY Screw_pair_with_range

           SUBTYPE OF (Screw_pair);

           lower_limit_actual_rotation : 
         OPTIONAL 
         plane_angle_measure;

           upper_limit_actual_rotation : 
         OPTIONAL 
         plane_angle_measure;
WHERE

           WR1: (NOT EXISTS(lower_limit_actual_rotation)
            OR
            NOT EXISTS(upper_limit_actual_rotation))
            XOR
            (lower_limit_actual_rotation < upper_limit_actual_rotation);

         
         END_ENTITY;


ENTITY Sliding_curve_pair

           SUBTYPE OF (Planar_curve_pair);

         
         END_ENTITY;


ENTITY Sliding_surface_pair

           SUBTYPE OF (Surface_pair);

         
         END_ENTITY;


ENTITY Spherical_pair

           SUBTYPE OF (Low_order_kinematic_pair);
DERIVE

           SELF\Low_order_kinematic_pair.t_x : BOOLEAN := FALSE;

           SELF\Low_order_kinematic_pair.t_y : BOOLEAN := FALSE;

           SELF\Low_order_kinematic_pair.t_z : BOOLEAN := FALSE;

           SELF\Low_order_kinematic_pair.r_x : BOOLEAN := TRUE;

           SELF\Low_order_kinematic_pair.r_y : BOOLEAN := TRUE;

           SELF\Low_order_kinematic_pair.r_z : BOOLEAN := TRUE;

         
         END_ENTITY;


ENTITY Spherical_pair_with_pin

           SUBTYPE OF (Low_order_kinematic_pair);
DERIVE

           SELF\Low_order_kinematic_pair.t_x : BOOLEAN := FALSE;

           SELF\Low_order_kinematic_pair.t_y : BOOLEAN := FALSE;

           SELF\Low_order_kinematic_pair.t_z : BOOLEAN := FALSE;

           SELF\Low_order_kinematic_pair.r_x : BOOLEAN := FALSE;

           SELF\Low_order_kinematic_pair.r_y : BOOLEAN := TRUE;

           SELF\Low_order_kinematic_pair.r_z : BOOLEAN := TRUE;

         
         END_ENTITY;


ENTITY Spherical_pair_with_pin_and_range

           SUBTYPE OF (Spherical_pair_with_pin);

           lower_limit_yaw : 
         OPTIONAL 
         plane_angle_measure;

           upper_limit_yaw : 
         OPTIONAL 
         plane_angle_measure;

           lower_limit_roll : 
         OPTIONAL 
         plane_angle_measure;

           upper_limit_roll : 
         OPTIONAL 
         plane_angle_measure;
WHERE

           WR1: (NOT EXISTS(lower_limit_yaw)
            OR
            NOT EXISTS(upper_limit_yaw))
            XOR
            (lower_limit_yaw < upper_limit_yaw);

           WR2: (NOT EXISTS(lower_limit_roll)
            OR
            NOT EXISTS(upper_limit_roll))
            XOR
            (lower_limit_roll < upper_limit_roll);

         
         END_ENTITY;


ENTITY Spherical_pair_with_range

           SUBTYPE OF (Spherical_pair);

           lower_limit_yaw : 
         OPTIONAL 
         plane_angle_measure;

           upper_limit_yaw : 
         OPTIONAL 
         plane_angle_measure;

           lower_limit_pitch : 
         OPTIONAL 
         plane_angle_measure;

           upper_limit_pitch : 
         OPTIONAL 
         plane_angle_measure;

           lower_limit_roll : 
         OPTIONAL 
         plane_angle_measure;

           upper_limit_roll : 
         OPTIONAL 
         plane_angle_measure;
WHERE

           WR1: (NOT EXISTS(lower_limit_yaw)
            OR
            NOT EXISTS(upper_limit_yaw))
            XOR
            (lower_limit_yaw < upper_limit_yaw);

           WR2: (NOT EXISTS(lower_limit_pitch)
            OR
            NOT EXISTS(upper_limit_pitch))
            XOR
            (lower_limit_pitch < upper_limit_pitch);

           WR3: (NOT EXISTS(lower_limit_roll)
            OR
            NOT EXISTS(upper_limit_roll))
            XOR
            (lower_limit_roll < upper_limit_roll);

         
         END_ENTITY;


ENTITY Su_parameters

           SUBTYPE OF (Detailed_geometric_model_element);

           a : length_measure;

           alpha : plane_angle_measure;

           b : length_measure;

           beta : plane_angle_measure;

           c : length_measure;

           gamma : plane_angle_measure;

         
         END_ENTITY;


ENTITY Surface_pair

           ABSTRACT SUPERTYPE
         
         OF (ONEOF (Sliding_surface_pair,
                                Rolling_surface_pair)
                        ANDOR Surface_pair_with_range)

           SUBTYPE OF (High_order_kinematic_pair);

           surface_1 : Surface;

           surface_2 : Surface;

           orientation : BOOLEAN;
WHERE

           WR1: SIZEOF( QUERY(r <* SELF\Kinematic_pair.associated_link_representations_1 | NOT(surface_1 IN r.items))) = 0;

           WR2: SIZEOF( QUERY(r <* SELF\Kinematic_pair.associated_link_representations_2 | NOT(surface_2 IN r.items))) = 0;

           WR3: SIZEOF( QUERY(lr <* SELF\Kinematic_pair.associated_link_representations_1 | 
            NOT('KINEMATIC_STRUCTURE_ARM.RIGID_LINK_REPRESENTATION' IN TYPEOF(lr)))) = 0;

         
         END_ENTITY;


ENTITY Surface_pair_with_range

           SUBTYPE OF (Surface_pair);

           range_on_surface_1 : Trimmed_surface;

           range_on_surface_2 : Trimmed_surface;

           lower_limit_actual_rotation : 
         OPTIONAL 
         plane_angle_measure;

           upper_limit_actual_rotation : 
         OPTIONAL 
         plane_angle_measure;
WHERE

           WR1: SELF\Surface_pair.surface_1 :=: range_on_surface_1.basis_surface;

           WR2: SELF\Surface_pair.surface_2 :=: range_on_surface_2.basis_surface;

           WR3: (NOT EXISTS(lower_limit_actual_rotation)
            OR
            NOT EXISTS(upper_limit_actual_rotation))
            XOR
            (lower_limit_actual_rotation < upper_limit_actual_rotation);

           WR4: SIZEOF( QUERY(r <* SELF\Kinematic_pair.associated_link_representations_1 | NOT(range_on_surface_1 IN r.items))) = 0;

           WR5: SIZEOF( QUERY(r <* SELF\Kinematic_pair.associated_link_representations_2 | NOT(range_on_surface_2 IN r.items))) = 0;

         
         END_ENTITY;


ENTITY Tool_attachment_point_frame

           SUBTYPE OF (Axis_placement_3d);
DERIVE

           SELF\Representation_item.name : label := ?;

         
         END_ENTITY;


ENTITY Tool_centre_point_frame

           SUBTYPE OF (Axis_placement_3d);
DERIVE

           SELF\Representation_item.name : label := ?;

         
         END_ENTITY;


ENTITY Unconstrained_pair

           SUBTYPE OF (Low_order_kinematic_pair);
DERIVE

           SELF\Low_order_kinematic_pair.t_x : BOOLEAN := TRUE;

           SELF\Low_order_kinematic_pair.t_y : BOOLEAN := TRUE;

           SELF\Low_order_kinematic_pair.t_z : BOOLEAN := TRUE;

           SELF\Low_order_kinematic_pair.r_x : BOOLEAN := TRUE;

           SELF\Low_order_kinematic_pair.r_y : BOOLEAN := TRUE;

           SELF\Low_order_kinematic_pair.r_z : BOOLEAN := TRUE;

         
         END_ENTITY;


ENTITY Universal_pair

           SUBTYPE OF (Low_order_kinematic_pair);

           input_skew_angle : 
         OPTIONAL 
         plane_angle_measure;
DERIVE

           SELF\Low_order_kinematic_pair.t_x : BOOLEAN := FALSE;

           SELF\Low_order_kinematic_pair.t_y : BOOLEAN := FALSE;

           SELF\Low_order_kinematic_pair.t_z : BOOLEAN := FALSE;

           SELF\Low_order_kinematic_pair.r_x : BOOLEAN := TRUE;

           SELF\Low_order_kinematic_pair.r_y : BOOLEAN := FALSE;

           SELF\Low_order_kinematic_pair.r_z : BOOLEAN := TRUE;

           skew_angle : plane_angle_measure := NVL (input_skew_angle, 0.0);

         
         END_ENTITY;


ENTITY Universal_pair_with_range

           SUBTYPE OF (Universal_pair);

           lower_limit_first_rotation : 
         OPTIONAL 
         plane_angle_measure;

           upper_limit_first_rotation : 
         OPTIONAL 
         plane_angle_measure;

           lower_limit_second_rotation : 
         OPTIONAL 
         plane_angle_measure;

           upper_limit_second_rotation : 
         OPTIONAL 
         plane_angle_measure;
WHERE

           WR1: (NOT EXISTS(lower_limit_first_rotation)
            OR
            NOT EXISTS(upper_limit_first_rotation))
            XOR
            (lower_limit_first_rotation < upper_limit_first_rotation);

           WR2: (NOT EXISTS(lower_limit_second_rotation)
            OR
            NOT EXISTS(upper_limit_second_rotation))
            XOR
            (lower_limit_second_rotation < upper_limit_second_rotation);

         
         END_ENTITY;


SUBTYPE_CONSTRAINT kps_property_definition_subtypes FOR Assigned_property;

           ONEOF (Product_definition_kinematics,
         Product_definition_relationship_kinematics);
      
         END_SUBTYPE_CONSTRAINT;


SUBTYPE_CONSTRAINT ks_axis_placement_3d_subtypes FOR Axis_placement_3d;

           ONEOF (Tool_attachment_point_frame,
         Tool_centre_point_frame);
      
         END_SUBTYPE_CONSTRAINT;


SUBTYPE_CONSTRAINT kss_representation_subtypes FOR Representation;

           ONEOF (Kinematic_link_representation,
         Kinematic_topology_structure,
         Kinematic_topology_directed_structure,
         Kinematic_topology_network_structure,
         Mechanism_representation,
         Geometric_model);
      
         END_SUBTYPE_CONSTRAINT;


FUNCTION collect_joints
 (items : SET[1:?] OF Pair_representation_relationship) : SET[0:?] OF Kinematic_joint;

LOCAL
  result : SET OF kinematic_joint := [];
END_LOCAL;
  REPEAT i := 1 TO HIINDEX(items);
    result := result + items[i].transformation_operator.joint;
  END_REPEAT;
  RETURN(result);


         END_FUNCTION;


FUNCTION representation_of_link
 (link : Kinematic_link) : Kinematic_link_representation;

RETURN (?);


         END_FUNCTION;


FUNCTION sort_link_associations
 (aprr : SET[1:?] OF Pair_representation_relationship; one_not_two : BOOLEAN) : SET[0:?] OF Kinematic_link_representation;

LOCAL
  result : SET OF Kinematic_link_representation := [];
END_LOCAL;
  IF one_not_two THEN
    REPEAT i := 1 TO HIINDEX(aprr);
      result := result + aprr[i].rep_1;
    END_REPEAT;
  ELSE  
    REPEAT i := 1 TO HIINDEX(aprr);
      result := result + aprr[i].rep_2;
    END_REPEAT;
  END_IF;
  RETURN(result);


         END_FUNCTION;



         END_SCHEMA;  -- Kinematic_structure_arm