9 Kinematic analysis control and result schema

9.1 General

The subject of the kinematic_analysis_control_and_result_schema is the identification and analysis of configurations of kinematic_structures and the interpolation between configurations. The schema covers the prescribed paths and the paths resulting from analysis.

Short names of entities defined in this schema are described in Annex A. Unambiguous identification of this schema is defined in Annex B.

REFERENCE FROM kinematic_motion_representation_schema    --  ISO 10303-105
  (link_motion_representation_along_path,
   interpolated_configuration_sequence);



REFERENCE FROM kinematic_topology_schema    --  ISO 10303-105
  (kinematic_joint);



REFERENCE FROM kinematic_structure_schema    --  ISO 10303-105
  (kinematic_link_representation,
   mechanism_representation,
   rigid_placement);



REFERENCE FROM geometry_schema    --  ISO 10303-42
  (geometric_representation_context);



REFERENCE FROM representation_schema    --  ISO 10303-43
  (representation,
   representation_relationship);



REFERENCE FROM measure_schema    --  ISO 10303-41
  (measure_with_unit,
   parameter_value);



REFERENCE FROM product_property_representation_schema    --  ISO 10303-41
  (shape_representation);
(*



NOTE 1   The schemas referenced above are specified in the following parts:

kinematic_motion_representation_schema	ISO 10303-105
kinematic_topology_schema	ISO 10303-105
kinematic_structure_schema	ISO 10303-105
geometry_schema	ISO 10303-42
representation_schema	ISO 10303-43
measure_schema	ISO 10303-41
product_property_representation_schema	ISO 10303-41

NOTE 2   See Annex D for a graphical representation of this schema.

9.2 Fundamental concepts and assumptions

A kinematic analysis is a specific presentation of the kinematic behaviour of a mechanical product. There are two possible ways to check the kinematic behaviour of a kinematic structure:

• forward analysis;
• backward analysis.

The forward analysis specifies the motion of a kinematic structure in terms of a sequence of configurations and of the interpolations between them. The result of a forward analysis is the path of specified frames on specified links.

The backward analysis specifies the motion of a kinematic structure with a prescribed path defined by frames. The result of a backward analysis is the sequence of configuration definitions in the form of the pair parameter values for a sufficiently large number of pairs to control the motion.

A configuration of a kinematic structure is defined by the specification of pair values for a set of pairs of the kinematic structure.

9.3 kinematic_analysis_control_and_result_schema type definitions

9.3.1 kinematic_analysis_definition   

EXPRESS specification:

*)
TYPE kinematic_analysis_definition = SELECT
   (interpolated_configuration_sequence,
    prescribed_path);
END_TYPE;
(*

9.3.2 kinematic_result   

EXPRESS specification:

*)
TYPE kinematic_result = SELECT
   (interpolated_configuration_sequence,
    resulting_path);
END_TYPE;
(*

9.4 kinematic_analysis_control_and_result_schema entity definitions

9.4.1 kinematic_analysis_consistency   

EXPRESS specification:

*)
ENTITY kinematic_analysis_consistency;
  control : kinematic_control;
  result : kinematic_analysis_result;
WHERE
  WR1: control.controlled_mechanism :=: result.analysed_mechanism;
END_ENTITY;
(*

Attribute definitions:

control: the kinematic_control providing the input for the analysis.

result: the kinematic_analysis_result which contains the results of the analysis.

Formal propositions:

WR1: Input and result data shall be related to the same mechanism_representation.

9.4.2 kinematic_analysis_result   

EXPRESS specification:

*)
ENTITY kinematic_analysis_result;
  analysed_mechanism : mechanism_representation;
  result : kinematic_result;
END_ENTITY;
(*

Attribute definitions:

analysed_mechanism: the mechanism_representation whose motion produced the results.

result: a motion, called result.

9.4.3 kinematic_control   

EXPRESS specification:

*)
ENTITY kinematic_control;
  controlled_mechanism : mechanism_representation;
  contained_kinematic_programs : kinematic_analysis_definition;
END_ENTITY;
(*

Attribute definitions:

controlled_mechanism: the mechanism_representation to which the control information applies.

contained_kinematic_programs: specifies the motion definition.

9.4.4 prescribed_path   

If the exact path cannot be achieved for any reason, any combination of joints may be used to achieve a path whose average distance from the prescribed path is minimized. If no controlling joints are given, any joints may be used to achieve the prescribed path.

EXPRESS specification:

*)
ENTITY prescribed_path
  SUBTYPE OF (link_motion_representation_along_path);
  controlling_joints : OPTIONAL SET[1:6] OF kinematic_joint;
END_ENTITY;
(*

Attribute definitions:

controlling_joints: an optional set of the kinematic_joints which are used to achieve the prescribed path motion. There shall exist at least one and at most six kinematic_joints for the prescribed_path.

NOTE    The individual degrees of freedom of a joint depend on the type of the pair that references the joint. Values to the degrees of freedom are assigned by the appropriate subtype of pair_value which always specifies values for all the individual degrees of freedom of a pair. On the other hand, the number of all individual degrees of freedom for the joints in the controlling_joints set must not exceed six in order to avoid the backward analysis problem becoming indeterminate. For this reason, if a pair with more than one degree of freedom (e.g., a cylindrical_pair) is associated with any joint in the controlling_joints set, the size of this set will be less than six.

9.4.5 resulting_path   

EXPRESS specification:

*)
ENTITY resulting_path
  SUBTYPE OF (link_motion_representation_along_path);
  controlling_joints : SET[1:?] OF kinematic_joint;
END_ENTITY;
(*

Attribute definitions:

controlling_joints: the kinematic_joints which have been used to achieve the resulting path motion. There shall exist at least one kinematic_joint for the resulting_path.

Informal propositions:

IP1: All the pairs which were used to achieve this resulting_path shall be given.

9.5 kinematic_analysis_control_and_result_schema subtype constraint definition

9.5.1 link_motion_representation_along_path_subtypes   

EXPRESS specification:

*)
SUBTYPE_CONSTRAINT link_motion_representation_along_path_subtypes FOR link_motion_representation_along_path;
  ONEOF (prescribed_path,
         resulting_path);
END_SUBTYPE_CONSTRAINT;
(*

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