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Application module:
Kinematic topology |
ISO/TS 10303-1799:2014-02(E)
© ISO
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This clause specifies the information requirements for the
Kinematic topology
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_topology_arm
schema and identifies the necessary external references.
EXPRESS specification:
*)
SCHEMA Kinematic_topology_arm;
(*
The following EXPRESS interface statements specify the elements
imported from the ARMs of other application modules.
EXPRESS specification:
*)
USE FROM
Elemental_topology_arm;
--
ISO/TS 10303-1005
USE FROM
Foundation_representation_arm;
--
ISO/TS 10303-1006
USE FROM
Part_view_definition_arm;
--
ISO/TS 10303-1023
USE FROM
Property_assignment_arm;
--
ISO/TS 10303-1030
REFERENCE FROM
Foundation_representation_arm
--
ISO/TS 10303-1006
(using_representations);
(*
NOTE 1
The schemas referenced above are specified in the following
part of ISO 10303:
| Elemental_topology_arm |
ISO/TS 10303-1005 |
| Foundation_representation_arm |
ISO/TS 10303-1006 |
| Part_view_definition_arm |
ISO/TS 10303-1023 |
| Property_assignment_arm |
ISO/TS 10303-1030 |
| Foundation_representation_arm |
ISO/TS 10303-1006 |
NOTE 2
See Annex C,
Figures
C.1and C.2
for a graphical representation of this schema.
This subclause specifies the ARM type
for this application module. The ARM type and
definition is specified below.
The kinematic_topology_representation_select type allows for the designation of the data
types
Kinematic_topology_structure, Kinematic_topology_directed_structure
and
Kinematic_topology_network_structure.
EXPRESS specification:
*)
TYPE
kinematic_topology_representation_select =
SELECT
(Kinematic_topology_structure,
Kinematic_topology_directed_structure,
Kinematic_topology_network_structure);
END_TYPE;
(*
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.
A Kinematic_joint is a type of
Edge
that is a specification of the topological aspect of an ordered connection between two and only two links.
A topological orientation is always implicitly associated with a joint.
This orientation is defined as being from the edge start to the edge end.
For a
Kinematic_pair
referencing a Kinematic_joint, the
transform_item_1
shall be an item of the
Kinematic_link_representation
of the edge_start of the Kinematic_joint.
Similarly, the
transform_item_2
shall be an item of the
Kinematic_link_representation
of the edge_end of the Kinematic_joint.
NOTE 1
The type of constraint on the relative motion is defined by the
Kinematic_pair
that has the joint as its
joint
attribute.
In a graph representation of the topology, the Kinematic_joint represents an
oriented edge connecting two vertices in the graph.
The orientation of the Kinematic_joint reflects an implicit orientation which is arbitrary,
except for the rack-and-pinion pair, the point-on-surface pair, and the point-on-planar-curve pair.
NOTE 2
If the sequence of edge_start and edge_end is interchanged, both, pair values and pair range
values, have to be used with the opposite signs
additionally the attributes giving a lower limit are to be interchanged with those giving the corresponding upper limit.
EXPRESS specification:
*)
ENTITY Kinematic_joint
SUBTYPE OF (Edge);
SELF\Edge.edge_start : Kinematic_link;
SELF\Edge.edge_end : Kinematic_link;
UNIQUE
UR1: edge_start, edge_end;
WHERE
WR1: edge_start :<>: edge_end;
END_ENTITY;
(*
Attribute definitions:
edge_start:
the link through which the joint is entered.
edge_end:
the link through which the joint is left.
Formal propositions:
UR1:
The combination of edge_start and edge_end shall be unique within a population of Kinematic_joint.
WR1:
The edge_start and edge_end shall not be identical.
A Kinematic_link is a type of
Vertex
representation of the topological aspects associated with a rigid part of a mechanism.
EXPRESS specification:
*)
ENTITY Kinematic_link
SUBTYPE OF (Vertex);
END_ENTITY;
(*
A Kinematic_loop is a type of
Edge_loop
that is a cycle in the subgraph.
It is the representation of a closed kinematic chain in a mechanism, where the last link in the chain is again connected
to the first
link by a joint.
The Kinematic_loop is analogous to the loop in the topology model, where the joints correspond to the edges and the links
correspond to the vertices of the topology model.
The loop shall be pointed to by at least one
Oriented_joint.
Every
Kinematic_joint
shall be oriented such that the list of
Kinematic_joints
have a common orientation within the loop.
NOTE
This entity is present in an instance of a kinematics model only if the kinematic structure takes the form of a directed
graph.
EXPRESS specification:
*)
ENTITY Kinematic_loop
SUBTYPE OF (Edge_loop);
SELF\Path.edge_list : LIST[1:?] OF
UNIQUE
Oriented_joint;
END_ENTITY;
(*
Attribute definitions:
edge_list:
an inherited attribute that shall be of type
Oriented_joint
There shall exist at least one
Oriented_joint
for the Kinematic_loop.
A Kinematic_property_definition_representation is a type of
Property_definition_representation
that relates a
Representation
to a
Product_definition_kinematics.
EXPRESS specification:
*)
ENTITY Kinematic_property_definition_representation
SUBTYPE OF (Property_definition_representation);
SELF\Property_definition_representation.definition : Product_definition_kinematics;
END_ENTITY;
(*
Attribute definitions:
definition:
an inherited attribute that shall be of type
Product_definition_kinematics.
A Kinematic_property_topology_representation is a type of
Kinematic_property_definition_representation
that relates a
kinematic_topology_representation_select
item
to a
Kinematic_link.
EXPRESS specification:
*)
ENTITY Kinematic_property_topology_representation
SUBTYPE OF (Kinematic_property_definition_representation);
SELF\Property_definition_representation.used_representation : kinematic_topology_representation_select;
base : Kinematic_link;
WHERE
WR1: SELF\property_definition_representation.used_representation IN using_representations(base);
END_ENTITY;
(*
Attribute definitions:
used_representation:
an inherited attribute that shall be of type
kinematic_topology_representation_select.
base:
the initial link of the Kinematic_property_topology_representation.
Formal propositions:
WR1:
The base shall be founded in the
kinematic_topology_representation_select.
A Kinematic_topology_directed_structure is a type of
Representation
that identified a directed structure within a parent
Kinematic_topology_structure.
EXPRESS specification:
*)
ENTITY Kinematic_topology_directed_structure
SUBTYPE OF (Representation);
SELF\Representation.items : SET[1:?] OF Oriented_joint;
parent : Kinematic_topology_structure;
WHERE
WR1: context_of_items :=: parent.context_of_items;
WR2: get_kinematic_joints_from_oriented_joints(items) <= parent.items;
END_ENTITY;
(*
Attribute definitions:
items:
an inherited attribute that shall be of type
Oriented_joint.
There shall exist at least one
Oriented_joint
for the Kinematic_topology_directed_structure.
parent:
the parent
Kinematic_topology_structure
in which this Kinematic_topology_directed_structure defines a direct subset.
Formal propositions:
WR1:
A Kinematic_topology_directed_structure shall have the same context as its parent.
WR2:
The
Oriented_joints
used by the items of a Kinematic_topology_directed_structure shall also be items of its parent.
A Kinematic_topology_network_structure is a type of
Representation.
A Kinematic_topology_network_structure represents a subgraph of network type; i.e., the mechanism is composed of closed kinematic chains.
NOTE 1
See
Figure 1
for an illustration of a kinematic network structure.
NOTE 2
This entity is present in an instance of a kinematics model only if the kinematic structure takes the form of a directed
graph.
Figure 1 — Example of a kinematic network structure
EXPRESS specification:
*)
ENTITY Kinematic_topology_network_structure
SUBTYPE OF (Representation);
SELF\Representation.items : SET[1:?] OF Kinematic_loop;
parent : Kinematic_topology_structure;
WHERE
WR1: context_of_items :=: parent.context_of_items;
WR2: get_kinematic_joints_from_kinematic_loops(items) <= parent.items;
END_ENTITY;
(*
Attribute definitions:
items:
an inherited attribute that shall be of type
Kinematic_loop.
There shall exist at least one
Kinematic_loop
for the Kinematic_topology_network_structure.
parent:
the parent
Kinematic_topology_structure
in which this Kinematic_topology_network_structure defines a subset with loops.
Formal propositions:
WR1:
A Kinematic_topology_network_structure shall have the same context as the parent.
WR2:
The
Oriented_joints
used by the items of a Kinematic_topology_network_structure shall also be items of its parent.
A Kinematic_topology_structure is a type of
Representation
that specifies the topological aspects of a kinematic representation.
The topology of the Kinematic_topology_structure is represented by means of
Kinematic_joints
which, in turn, establish a relationship between pairs of
Kinematic_links.
NOTE
Every kinematic structure can be described in terms of its joints and links.
Joints constrain the motion between two rigid objects called links.
Joints and links are sufficient to describe the topology of kinematic structures,
but for computation it is meaningful to introduce additional levels of structure based on graph theory.
Information related to the graph representation of a kinematic structure is given in
Kinematic_topology_substructure.
EXPRESS specification:
*)
ENTITY Kinematic_topology_structure
SUBTYPE OF (Representation);
SELF\Representation.items : SET[1:?] OF Kinematic_joint;
WHERE
WR1: SIZEOF (QUERY (item <* items | 'FOUNDATION_REPRESENTATION_ARM.ORIENTED_EDGE' in TYPEOF(item))) = 0;
END_ENTITY;
(*
Attribute definitions:
items:
the set of
Kinematic_joints
that compose the Kinematic_topology_structure of a mechanism.
There shall exist one or more
Kinematic_joints
for the Kinematic_topology_structure.
Formal propositions:
WR1:
None of the items shall be an
Oriented_edge.
A Kinematic_topology_substructure is a type of
Kinematic_topology_structure
that specifies the topological characteristics of a mechanism in terms of tree or network structures.
NOTE 1
Using graph theory, the topology of a mechanism is represented by a directed graph, where the links correspond to the nodes,
and the joints correspond to the edges.
This graph can be derived from the definition of the links and joints.
If the topology of a mechanism is defined only by this minimal information, it is referred to as "lower level topology"
within this part of ISO 10303.
Graph theory provides a means to capture connectivity information which may be applied to the describe
the topological structure of mechanisms.
The geometrical and mechanical properties are not conveyed.
If the full topological information including connectivity information is provided explicitly,
this is referred to as "higher level topology" within this part of ISO 10303.
A general graph may be composed of two basic types of subgraphs:
- Trees;
- Networks.
If, in addition to the lower level of topology, the higher level topology is provided in a kinematic model,
this higher level of topology is represented by kinematic substructures.
These kinematic substructures are:
-
a kinematic tree structure, whose graph representation is a single oriented tree and which consists
only of oriented kinematic joints connecting the kinematic links;
-
a kinematic network structure, whose graph representation consists of oriented kinematic loops.
NOTE 2
See [4]? for methods that can be applied to analyze a kinematic topology substructure.
EXPRESS specification:
*)
ENTITY Kinematic_topology_substructure
SUBTYPE OF (Kinematic_topology_structure);
parent : Kinematic_topology_structure;
WHERE
WR1: SELF\Representation.context_of_items :=: parent\Representation.context_of_items;
WR2: SELF\Representation.items <= parent\Representation.items;
END_ENTITY;
(*
Attribute definitions:
parent:
the
Kinematic_topology_structure
of which the Kinematic_topology_substructure forms a component.
Formal propositions:
WR1:
A Kinematic_topology_substructure shall have the same context as the parent.
WR2:
The
items
of a Kinematic_topology_substructure shall also be
items
of the parent.
A Kinematic_topology_tree_structure is a type of
Kinematic_topology_directed_structure.
A Kinematic_topology_tree_structure represents a subgraph of tree type; i.e., the mechanism is composed of open kinematic chains.
NOTE 1
See
Figure 2
for an illustration of a kinematic topology tree structure.
NOTE 2
This entity is present in an instance of a kinematics model only if the kinematic topology structure takes the form of a
directed graph.
Figure 2 — Example of a kinematic topology tree structure
EXPRESS specification:
*)
ENTITY Kinematic_topology_tree_structure
SUBTYPE OF (Kinematic_topology_directed_structure);
END_ENTITY;
(*
An Oriented_joint is a type of
Oriented_edge
that is a direction of traversal of a joint.
NOTE
This entity is present in an instance of a kinematics model only if the kinematic structure takes the form of a directed
graph.
EXPRESS specification:
*)
ENTITY Oriented_joint
SUBTYPE OF (Oriented_edge);
SELF\Oriented_edge.edge_definition : Kinematic_joint;
END_ENTITY;
(*
Attribute definitions:
edge_definition:
an inherited attribute that shall be of type
Kinematic_joint.
A Product_definition_kinematics is a type of
Assigned_property.
The Product_definition_kinematics specifies the kinematic property of a product.
EXPRESS specification:
*)
ENTITY Product_definition_kinematics
SUBTYPE OF (Assigned_property);
SELF\Assigned_property.described_element : Part_view_definition;
INVERSE
representation_relation : Kinematic_property_definition_representation FOR definition;
UNIQUE
UR1: described_element;
END_ENTITY;
(*
Attribute definitions:
described_element:
an inherited attribute that shall be of type
Part_view_definition.
representation_relation:
specifies an inverse relationship that specifies that the existence of the Product_definition_kinematics is dependent on the existence of the
Kinematic_property_definition_representation
that specifies the Product_definition_kinematics as its
definition.
Formal propositions:
UR1:
The described_element shall be unique within a population of Product_definition_kinematics.
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.
The
kts_representation_subtypes
constraint specifies a constraint that applies to instances of subtypes of
Representation.
EXPRESS specification:
*)
SUBTYPE_CONSTRAINT kts_representation_subtypes FOR Representation;
ONEOF (Kinematic_topology_structure,
Kinematic_topology_directed_structure,
Kinematic_topology_network_structure);
END_SUBTYPE_CONSTRAINT;
(*
This subclause specifies the ARM functions for
this module. The ARM functions and definitions are
specified below.
The get_kinematic_joints_from_kinematic_loops function returns the set of
Kinematic_joints
associated with the
Kinematic_loop
as a kls.
EXPRESS specification:
*)
FUNCTION get_kinematic_joints_from_kinematic_loops (kls : SET[0:?] OF Kinematic_loop) : SET[0:?] OF Kinematic_joint;
LOCAL
result : SET OF Oriented_joint := [];
END_LOCAL;
IF SIZEOF(kls) > 0 THEN
REPEAT i := 1 TO HIINDEX(kls);
result := result + kls[i].edge_list;
END_REPEAT;
END_IF;
RETURN (get_kinematic_joints_from_oriented_joints(result));
END_FUNCTION;
(*
Argument definitions:
kls:
the specified set of
Kinematic_loops.
The get_kinematic_joints_from_oriented_joints function returns the set of
Kinematic_joints
associated with the
Oriented_joint
as a ors.
EXPRESS specification:
*)
FUNCTION get_kinematic_joints_from_oriented_joints (ors : SET[0:?] OF Oriented_joint) : SET[0:?] OF Kinematic_joint;
LOCAL
result : SET OF Kinematic_joint := [];
END_LOCAL;
IF SIZEOF(ors) > 0 THEN
REPEAT i := 1 TO HIINDEX(ors);
result := result + ors[i].edge_definition;
END_REPEAT;
END_IF;
RETURN (result);
END_FUNCTION;
(*
Argument definitions:
ors:
the specified set of
Oriented_joints.
*)
END_SCHEMA; -- Kinematic_topology_arm
(*
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