Model Element

Description

Constraint_Jprim is used to remove degrees of freedom between two bodies by specifying conditions in which the relative translational or rotational motion can occur.

Constraint_Jprim differs from Constraint_Joint in that the former specifies mathematical constraints which may not have concrete physical realizations like the latter.

Format

<Constraint_Jprim

   id           = "integer"

  [label        = "string"]

   i_marker_id  = "integer"

   j_marker_id  = "integer"

   type         = {

                   "ATPOINT"

                   "INLINE"

                   "INPLANE"

                   "ORIENTATION"

                   "PARALLEL_AXES"

                   "PERPENDICULAR"

                  }

/>

Attributes

id

Element identification number, (integer>0).  This is a number that is unique among all Constraint_Jprim elements. This parameter is required.

label

The name of the Constraint_Jprim element.  This is a character string.

i_marker_id

Specifies a Reference_Marker that defines the connection on the first body.  The body may be a rigid body, a flexible body, or a point body.  This parameter is required.

j_marker_id

Specifies a Reference_Marker that defines the connection on the first body.  The body may be a rigid body, a flexible body, or a point body. This parameter is required.

type

Specifies the type of constraint between the i_marker_id and j_marker_id. Type may be one of the following:

This parameter is required.

See Comments for more information about these primitive types.

Comments

The internal reaction forces and moments at each Reference_Marker of the primitive obey Newton’s third law of motion. Their magnitude and direction is such that they cancel each other out as shown in Figure 1 below.

Figure 1: Internal force and torque balance in a Constraint_Jprim

Figure 2: A simple system with redundant constraints

Both the door as well as the frame are assumed to be rigid.  Three hinges connect the door to the frame, allowing the door to open and close.  The hinges are modeled as revolute joints.  In this idealization, the hinges are assumed to be massless and rigid.  Each hinge allows rotation between the door and the frame about an axis, shown as a red arrow in Figure 3:

In this idealization, a few points should be noted:

If such a system is provided to MotionSolve, it will detect a redundancy in the constraints and remove the equivalent of two hinges from the model.  It will solve the system so that the correct motion is predicted.

The effect of removing two hinges from the solution process is to set their reaction forces to zero.  Clearly, this is unexpected behavior.  In reality, all three hinges have reaction forces and torques.  This is an issue with the idealization of the system.  If at least one of two bodies, the door or the frame, were made flexible, then more realistic reactions would be observed at each hinge.

This is a constraint primitive that requires that the origin of a Reference_Marker on Body-2 stay superimposed on the origin of the Reference_Marker placed on Body-1.  All rotations are allowed but no translations are allowed.  Figure 3 shows a schematic of an ATPOINT constraint primitive.

Figure 3: A schematic of an ATPOINT constraint primitive

This is a constraint primitive that requires that the origin of a Reference_Marker on Body-1 translates along the z-axis of a Reference_Marker placed on Body-2.  All rotations are allowed.  Figure 4 shows a schematic of an INLINE primitive.

Figure 4: A schematic of an INLINE primitive

The inline primitive constrains two translational degrees of freedom.  It prohibits translation along the x- and y-axes of the Reference_Marker on Body-2.

This is a constraint primitive that requires that the origin of a Reference_Marker on Body-1 (I in the figure below) to stay in the XY plane defined by the origin of the J Reference_Marker and its z-axis.  Figure 5 shows a schematic of an INPLANE primitive.

Figure 5: A schematic of an INPLANE primitive

The INPLANE primitive constrains one translational degree of freedom.  It prohibits translation along the z-axis of the Reference_Marker J on Body-2.  All rotations are allowed.

Figure 6 shows a schematic of an ORIENTATION primitive.  It requires that the orientation of a Reference_Marker on Body-1 (I in the figure below) always be the same as the orientation of a Reference_Marker on Body-2 (J in the figure below).

Figure 6: An ORIENTATION primitive

The ORIENTATION primitive removes three degrees of freedom; all of these are rotational.  All three translations of Body-1 with respect to Body-2 are allowed.

Figure 7 shows a schematic of a PARALLEL_AXES primitive.  This primitive constrains Body-1 such that the z-axis of a Reference_Marker (I in the figure below) is always parallel to the z-axis of a Reference_Marker on Body-2 (J in the figure below).

Figure 7 A PARALLEL_AXES primitive

The PARALLEL_AXIS primitive removes two rotational degrees of freedom.  Rotation of Body-1 is only allowed about the z-axis of the J Reference_Marker. All three translations are allowed.

Figure 8 shows a schematic of a PERPENDICULAR_AXES primitive.  This primitive constrains Body-1 such that the z-axis of a Reference_Marker (I in the figure below) is always PERPENDICULAR to the z-axis of a Reference_Marker on Body-2 (J in the figure below).

Figure 8: A PERPENDICULAR_AXES primitive

The PERPENDICULAR_AXIS primitive removes one degree of freedom.  Rotation of Body-1 is only allowed about the z-axis of the I Reference_Marker and the z-axis of the J Reference_Marker. All three translations are allowed.

Example

Following is an implementation of a Constraint_Jprim of type INPLANE:

<Constraint_Jprim

    id                  = "301001"

    type                = "INPLANE"

    i_marker_id         = "30102021"

    j_marker_id         = "30103020"

/>

Model Element

Description

JPRIM is used to remove degrees of freedom between two bodies by specifying conditions in which the relative translational or rotational motion can occur. JPRIM differs from JOINT in that the former specifies mathematical constraints, which may not have concrete physical realizations like the latter.

Declaration

def JPRIM(id, LABEL="", I=0, J=0, TYPE="ATPOINT"):

Attributes

id

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

LABEL

The name of the JPRIM element.  This is a character string.

I

Specifies the ID of the reference marker that defines the connection on the first body.  The body may be a rigid body, a flexible body, or a point body.  The parameter is required.

J

Specifies the ID of the reference marker that defines the connection on the second body.  The body may be a rigid body, a flexible body, or a point body.  The parameter is required.

TYPE

Specifies the type of constraint connection between the i_marker and j_marker_id.  The type could be one of the following:

"ATPOINT"

"INLINE"

"INPLANE"

"ORIENTATION"

"PARALLEL_AXES"

"PERPENDICULAR"

Comments

See Constraint_JPRIM

Example

The example below is an implementation of a JPRIM of type "INPLANE."

JPRIM(301001,LABEL="Joint 1",I=30102021,J=30103020,TYPE="INPLANE")