Constraint: SFSF

Model Element

Description

Constraint_SFSF defines a higher pair constraint. The constraint consists of a surface on one body rolling and sliding on a surface on a second body. The surfaces are required to have a unique contact point.

Format

<Constraint_SFSF

id = "integer"

label = “Name of Constraint_SFSF element”

i_marker_id = "integer"

i_surface_id = "integer"

i_disp_x0 = "real"

i_disp_y0 = "real"

i_disp_z0 = "real"

j_marker_id = "integer"

j_surface_id = "integer"

j_disp_x0 = "real"

j_disp_y0 = "real"

j_disp_z0 = "real"

</Constraint_SFSF>

Attributes

Element identification number (integer>0). This number is unique among all Constraint_SFSF elements.

label

The name of the Constraint_SFSF element.

i_marker_id

Specifies a marker that defines the coordinate system in which the i_surface points are defined. It also implicitly defines the body on which the surface is "etched". The surface moves with the body. i_marker_id may belong to any type of body: flexible, rigid, or point. The parameter is mandatory.

i_surface_id

Specifies the ID of the Reference_ParamSurface that contains the surface definition.

i_disp_x0

i_disp_y0

i_disp_z0

These three parameters specify the location of the contact point on i_surface at the input configuration as measured in the i_marker_id coordinate system. The three parameters come as a set. All three must be specified or none may be defined. These parameters are optional. See Comment 8 for more details.

j_marker_id

Specifies a Reference_Marker that defines the coordinate system in which the j_surface points are defined. It also implicitly defines the body on which the surface is "etched". The surface moves with the body. j_marker_id may belong to any type of body: flexible, rigid, or point. The parameter is mandatory.

j_surface_id

Specifies the ID of the Reference_ParamSurface that contains the surface definition.

j_disp_x0

j_disp_y0

j_disp_z0

These three parameters specify the location of the contact point on j_surface at the input configuration as measured in the j_marker_id coordinate system. The three parameters come as a set. All three must be specified or none may be defined. These parameters are optional. See Comment 8 for more details.

Comments

1.	Constraint_SFSF element constrains the two surfaces as follows:

•	They surfaces have exactly one contact point,

•	The normal at the contact point for each surface are anti-parallel.

This is shown schematically in Figure 2 below. Pi and Pj represent the contact point on the two surfaces I and J respectively. Ni and Nj are the normals at the contact point for Surface I and Surface J respectively. The contact conditions are shown mathematically in the box at the bottom-left.

CSFSFComFig1

The contact condition between two surfaces

The surface-to-surface constraint does not allow lift-off. You can examine the sign of the constraint force to determine if any lift-off should have occurred if the constraint were not there. A positive value implies that the force is repulsive. A negative value implies an attractive force. The surfaces would separate if the constraint were not present. If your results require an accurate simulation of intermittent contact, you should model the contact forces directly using a Force_Contact or a Force_TwoBody object.

3.	Both open and closed surfaces supported by Constraint_SFSF.

Open surfaces have a well defined spatial extent. The surface is only defined in the domain αmin <= α <= αmax, and βmin <= β <= βmax where α and β are the surface parameters. While enforcing the surface-to-surface constraint, it is possible for MotionSolve to find a solution outside this range. It is your responsibility to define appropriate forces at the surface ends, so that the contact point stays in the legal range for α and β.

5.	The surfaces in a Constraint_SFSF are required to have a single point of contact. Convex surfaces will guarantee a single point of contact. A convex surface is one that intersects a straight line at just two points. See Figure 3 below for examples of convex and non convex shapes.

6.	The oval shaped closed surface on the left is an example of a convex shape. Notice that any straight line can intersect the surface at only two points. In contrast, the open surface on the right is non-convex. You can draw a straight line that intersects it at more than two points.

CSFSFComFig2

Convex and Non-Convex surfaces

7.	Be suspicious of the correctness of your model, if ever one of the constraints belonging to a Constraint_SFSF is declared to be redundant. This will lead to unexpected behavior and is a sure indication that the model has not been correctly built.

8.	MotionSolve does an initial search to exactly locate the contact point. While the attributes i_disp_x0, i_disp_y0, i_disp_z0, j_disp_x0, j_disp_y0, and j_disp_z0 are not mandatory, it is a good idea to specify them if you know what they are.

Example

Figure 1 below shows two surfaces I and J that are in continuous contact.

CSFSF_ExFig1

Surface-to-Surface Contact

Surface I is defined with respect to Reference_Marker 1023; surface J is defined with respect to Reference_Marker 2046. Reference_ParamSurface 123 defines surface I and Reference_ParamSurface 246 defines surface J. The patch containing the contact point is also shown in figure 1.

An initial guess for the contact point on both surfaces is defined. Assume the initial contact point location on surface J, as measured in the coordinate system of 2046, is [1.466, 5.66, 0.1]. Assume the contact point location on surface I, as measured in the coordinate system of 1023, is [-0.522, -0.852, -0.453].

The Constraint_SFSF object may be defined as follows:

<Constraint_SFSF

id = "1"

i_marker_id = "1023"

i_surface_id = "123"

i_disp_x0 = "1.466"

i_disp_y0 = "5.66"

i_disp_z0 = "0.1"

j_marker_id = "2046"

j_surface_id = "246"

j_disp_x0 = "-0.522"

j_disp_y0 = "-0.852"

j_disp_z0 = "-0.452" >

</Constraint_SFSF>

Model Element
Description
SFSF defines a higher pair constraint. The constraint consists of a surface on one body rolling and sliding on a surface on a second body. The surfaces are required to have a unique contact point.
Declaration
def SFSF(id, LABEL="", ISURFACE=0, IRM=0, JSURFACE=0, JRM=0, IDISP=[0.0,0.0,0.0], JDISP=[0.0,0.0,0.0]):
Attributes
id	Element identification number (integer>0). This number is unique among all the SFSF elements.
LABEL	The name of the SFSF element.
ISURFACE	Specifies the ID of the surface that is fixed to the first body.
IRM	Specifies the ID of a fixed marker that defines the coordinate system in which the ISURFACE points are defined. It also implicitly defines the body on which the surface is "etched". The surface moves with the body.
JSURFACE	Specifies the ID of the surface that is fixed to the second body.
JRM	Specifies the ID of a fixed marker that defines the coordinate system in which the JSURFACE points are defined. It also implicitly defines the body on which the surface is "etched". The surface moves with the body.
IDISP	These three parameters specify the location of the contact point on ISURFACE at the input configuration as measured in the IRM coordinate system. The three parameters come as a set. All three must be specified or none may be defined. These parameters are optional.
JDISP	These three parameters specify the location of the contact point on JSURFACE at the input configuration as measured in the JRM coordinate system. The three parameters come as a set. All three must be specified or none may be defined. These parameters are optional.
Comments See Constraint_SFSF
Example The example below shows how a SFSF may be defined. SFSF(1,LABEL="SFSF", ISURFACE=123,IRM=1023, JSURFACE=246,JRM=2046,IDISP=[1.466,5.66,0.1], JDISP=[-0.522,-0.852,-0.453])

Constraint: SFSF

Constraint: SFSF

Constraint: SFSF

Model Element

Description

Format

Attributes

Comments

Example

Model Element

Description

SFSF defines a higher pair constraint. The constraint consists of a surface on one body rolling and sliding on a surface on a second body. The surfaces are required to have a unique contact point.

Declaration

Attributes

id

Element identification number (integer>0). This number is unique among all the SFSF elements.

LABEL

The name of the SFSF element.

ISURFACE

Specifies the ID of the surface that is fixed to the first body.

IRM

Specifies the ID of a fixed marker that defines the coordinate system in which the ISURFACE points are defined. It also implicitly defines the body on which the surface is "etched". The surface moves with the body.

JSURFACE

Specifies the ID of the surface that is fixed to the second body.

JRM

Specifies the ID of a fixed marker that defines the coordinate system in which the JSURFACE points are defined. It also implicitly defines the body on which the surface is "etched". The surface moves with the body.

IDISP

These three parameters specify the location of the contact point on ISURFACE at the input configuration as measured in the IRM coordinate system.

The three parameters come as a set. All three must be specified or none may be defined.

These parameters are optional.

JDISP

These three parameters specify the location of the contact point on JSURFACE at the input configuration as measured in the JRM coordinate system. The three parameters come as a set. All three must be specified or none may be defined.

These parameters are optional.

Comments

See Constraint_SFSF

Example

The example below shows how a SFSF may be defined.