5.5 Overview On Different Joint Definitions · 2016. 3. 25. · 3 DOF – 1 algebraic constraint = 2 DOF Thus, there are two degrees-of-freedom in this system, and any two will prescribe

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MotionView / MotionSolve Fundamentals

5.5 Overview On Different Joint DefinitionsIn MotionView you can create 27 types of Joints. As shown in the figure below, the 27 Joints can be classified into five main categories.

Classification Of Joints That Can Be Created In MotionView

Lower Pair Constraints - A lower pair is an ideal joint that constrains contact between a point, line or plane in the moving body to a corresponding point, line or plane in a fixed body or another moving body. These have physical analogies (e.g., a revolute joint).

Joint Primitives – Joint Primitives constrain combination of individual degrees of freedom between bodies. In most cases there are no mechanical equivalents for Joint Primitives.

Higher Pair Constraints - In Higher pair constraints, the two bodies are in contact at a point or along a line, as in a ball bearing or disk cam and follower and the relative motions of coincident points are not same.

Motion as a Constraint – A Motion is a prescribed displacement, velocity or acceleration on a body along a specified direction. When a motion is applied on a body the free degrees of freedom of the body are replaced by the prescribed movement as specified by the motion, thus a Motion is considered as constraint.

Other Joints – This classification consists of constraints which are used to specify algebraic relations between two or more joints.

In the table below an overview on different Joints and Joint Definitions is provided.

G1 and G2 Geometric grid point identification number. Used to identify the bodies to be connected and, for many JTYPEs, the location of the joint.

G1 and G2 identify the bodies being joined and must, therefore, belong to different bodies.

X3, Y3, Z3 First orientation vector of the joint.

X4, Y4, Z4 Second orientation vector of the joint.

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Ball

Revolute

Translational

Cylindrical

Fixed

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Continuation of Joint Types

Planar

Inline

Perpendicular

Parallel

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Continuation of Joint Types

G1 and G2 Geometric grid point identification number. Used to identify the bodies to be connected and, for many JTYPEs, the location of the joint.

G1 and G2 identify the bodies being joined and must, therefore, belong to different bodies.

X3, Y3, Z3 First orientation vector of the joint.

X4, Y4, Z4 Second orientation vector of the joint.

Orient

Inplane

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Joint / Creation

As right mouse click on the Joint symbol opens up the Add Joint or JointPair dialogue window.

Add Joint Or Joint Pair Dialogue

Hint: The recommended naming convention for creating joints is that all joint variable names start with j_. Further the variable name can be descriptive but should not contain any special characters other than an underscore. Again you may use the same name for Label and Variable, e.g. j_cylindrical

A joint entity (like most of the entities that are created in MotionView) can be a Single Entity or a Pair Entity. The pair entities help in creating models which are symmetric about the Z-X Plane of the model (i.e. the Y property is mirrored).

Compliant Joints: Compliant joints are identical to bushings and allow relative motion in all six degrees freedom. The relative motion will be dependent on the stiffness and damping of the compliant joint. In order for a joint to be compliant, the Allow compliance option must be enabled at the time of joint creation. This option also allows you to switch back to an idealized constraint. However, you cannot switch to a compliant joint if you started with a joint that is not defined as compliant.

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Example: Adding a revolute joint

We now will add a revolute joint to the body shown in the image below. The body was assigned a primitive geometry of type cylinder before. Here, the aim is to create a simple pendulum.

This joint must be connected to two bodies.

Location: Point 0 (lower left Point in image)

Rotation axis: global y-direction

Body 1 corresponds to the (green) body named Free Body

Body 2 = Ground Body.

With this information it is straight forward to complete the definition of the revolute joint as shown below:

Zoom in on the graphic to confirm the direction of the joint – Z-axis points in the direction of the rotational degree of freedom, here global y-axis.

Note: The Revolute Joint removes 5 degree of freedom (only rotation wrt to the z-axis is permitted). Note also that Displacement Initial Condition for Joints is not supported by MotionSolve as of version 12.0. Only Velocity Initial condition is supported.

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5.5.1 ConstraintsA joint represents a constraint on the bodies that are connected to it. A revolute joint, for example, only leaves 1 dof free – the bodies can only rotate with respect to each other about the axis of rotation of the joint. The 6 lower pairs are essential for modeling. Higher pairs are not essential, since they do not form a finite set. In the absence of available elements, they can sometimes be constructed using combinations of other building blocks.

Constraint Definition: Joints and Motions

Joints and motions in MotionView/MotionSolve are constraints – this word has a specific meaning in MBD, and this means that these are algebraic equations that restrict the relative motion between bodies. In other words, constraints only allow the two connected bodies to have relative motion in certain specific directions. Motion in all the other directions is prohibited, and the system is “constrained” not to move in those directions.

Constraints generally restrict two types of motion:

• Translational

• Rotational

Dependence on Time

Constraints are classified in several ways. One key classification is based on whether the constraint depends explicitly on time

• Constraints without explicit time dependence are used to model joints, such as the ball and socket joint and the universal joint.

• Constraints with explicit time dependence are used to represent prescribed motions into the system, such as the constant speed spinning motion of a turbine.

Constraint Reaction Forces/Torques

Each constraint introduces, internally, constraint forces and/or moments that enforce the algebraic relationship of the constraint. These constraint forces and moments can be computed using MotionSolve to obtain the loads acting through the connections in your mechanism. In the case of prescribed motions, the constraint forces provide driving forces and moments which are useful in estimating the capacity required of actuators to achieve those motions.

Constraints Need Markers

Markers are required for the definition of a joint or motion in order to restrict the relative motion between the bodies. A marker on one body is called the I-marker, and it must be restrained relative to the marker on the other body (called the J-marker). Since the marker is fixed to the body, the body is then constrained by the joint.

For example, consider a spherical joint (also known as a ball joint).

A SPHERICAL Joint

This joint constrains two Reference_Markers, I on Body-1 and J on Body-2, such that their origins Oi and Oj are always superposed.

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The SPHERICAL joint removes three degrees of freedom from a system. Body-2 is allowed to rotate with respect to Body-1. Relative translation is not allowed.

Note: Notice that the Z-axis is usually the “funny” axis that defines the behavior of the joint, e.g, the axis of rotational freedom for the revolute joint and the axis of translational freedom for the translational joint.

Constraints Remove Degrees of Freedom

We have previously discussed that constraints are made up of joints and motions, and these constraints are a set of algebraic constraints.

Restriction of motion means that degrees-of-freedom are removed by constraints, since they are represented by algebraic equations that relate the bodies coordinates to one-another in some fashion.

For example, say you have three independent variables, x, y, Theta (3 DOF), as you would have in a planar system:

Then if you have an algebraic equation that relates them:

x – y = 0

This means that y depends on x, and vice versa. For example, if you specify x = 3, then y must be equal to 3 based on our algebraic constraint. (this is basically as translational constraint in planar space)

3 DOF – 1 algebraic constraint = 2 DOF

Thus, there are two degrees-of-freedom in this system, and any two will prescribe the system configuration (it doesn’t matter which you choose). This same concept is true of all of the constraints in MotionView/MotionSolve in three dimensional space.

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The summary provided below is extremely helpful to determine the DOF’s of the MBD system

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5.5.3 Joint PrimitivesJoint Primitives (JPRIM’s) are just like joints in that they remove translational and rotational DOF from bodies, but these do not necessarily have a direct physical analogy, outside of an ATPOINT jprim, which is identical to a ball joint. JPRIM’s are often used in combination with other joints to model systems without introducing redundant constraints. They also can be used to model more complicated mechanisms.

The Table below shows the list of joint primitives that can be created in MotionView along with the DOF that each joint primitive removes.

List Of Constraints And DOF Removed By Each Constraint

Joint Primitives (JPRIM) Example - INPLANE

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. The Figure below shows 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.

This joint is often used in a two or four-post testrig for suspensions. This INPLANE jprim keeps the wheel in the plane of the testrig platen for motion in jounce and rebound, but allows the wheel to rotate in any direction and to move fore-aft (x-direction) and laterally (y-direction).

Notice again that the z-axis of the marker is the “funny” axis that describes the behavior of the constraint.

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5.5.4 Higher Pair Constraints

Higher pair constraints are just like joints in that they remove translational and rotational DOF from bodies. The table below shows the list of higher pair constraints that can be created in MotionView along with the DOF that each joint primitive removes.

List Of Higher Pair Constraints

There are only 6 lower pairs, but any number of higher pairs can be constructed. Several higher pairs are fairly esoteric, which means their applications are restricted to specific domains. Modeling elements for tires, for instance, are called for almost exclusively by vehicle-dynamics designers. Some higher pairs can be constructed using simpler modeling elements, if the modeling tool supports programmatic control. For instance, a one-way clutch can be modeled using a bush together with an “if” statement to change properties based on the direction of rotation (MotionView provides support both for bushes and for programmatic control).

In higher pair constraints, the two bodies are in contact at a point or along a line, as in a ball bearing or disk cam and follower and the relative motions of coincident points are not same.

Recall the Definitions: Lower Pair Constraints - A lower pair is an ideal joint that constrains contact between a point, line or plane in the moving body to a corresponding point, line or plane in a fixed body or another moving body. These have physical analogies (e.g., a revolute joint).

Joint Primitives – Joint Primitives constrain combination of individual degrees of freedom between bodies. In most cases there are no mechanical equivalents for Joint Primitives.

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5.5.5 Curve-to-Curve (CVCV) ConstraintThe curve-to-curve constraint is useful for modeling cams where the point of contact between two parts changes during the motion of the system. The curves always maintain contact, however, even when the physics of the model might dictate that one curve lift off the other. You can examine the constraint forces to determine if any lift-off should have occurred.

Degrees of Freedom Removed

The curve-curve constraint removes three degrees of freedom from the system. When the body of the first curve is fixed in space, the second curve is allowed to move in three ways:

• It can slide along the first curve,

• roll on the first curve, and

• rotate about the common tangent at the point of contact.

The curve-to-curve constraint does not enforce the condition that the curves remain coplanar. One or both of the curves may be 3D curves. The curves can rotate about the common tangent at the point of contact, therefore they can move out of plane even when both curves are planar curves. Both open and closed curves supported.

Two higher-pairs that are extremely common are cams and gears.

Cams

A cam rotates about an axis and pushes a follower. The cam usually rotates at a uniform speed, and the profile of the cam is chosen so as to deliver the required motion to the follower. There are various classifications of both cams and followers, most of which reflect the topology or shape of the respective elements. The follower is usually spring loaded to ensure that it stays in contact with the cam all through the rotation cycle.

I Image from http://en.wikipedia.org/wiki/Cam

Design interest centers principally around two things:

1. the profile the cam should have to achieve a required motion – the rise, dwell and return

2. the velocities and accelerations of the follower, and the resulting forces on the various components in the assembly

The first is usually the more interesting problem, but the second is no less challenging. Sometimes the cam profile is determined to match a specified follower-motion, but such cams can be expensive to manufacture. Often a predetermined cam profile is chosen and the follower of the motion is to be determined so that the design of the rest of the assembly can be tailored accordingly.

The joint between the cam and its follower is maintained by contact. General contact can be used, but this approach is subject to the difficulties discussed in the Chapter on Contact. It is usually more computationally efficient to use point-to-curve (PTCV) or point-to-surface (PTSF) constraints. This approach does sacrifice some of the generality offered by a full-fledged contact model. For instance, the PTCV constraint does not allow for contact to be broken. But at the concept design stage, the analysis is usually a kinematic analysis, since the goal is to derive the required profile of the cam.

Once this is done constraints like the PTCV can be used to verify that there has been no loss of contact. If there is indeed loss of contact, full fledged contact modeling is essential. Contact between the cam and follower can break if the spring-load is not enough to compensate for the inertial forces (that is, forces due to the accelerations the bodies experience). In engine-design this is commonly called valve float, because cams are mainly used in the engine to control the valve timing of four-stroke engines. The term lift-off is also used in several applications.

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Gears

There are two distinct problems posed by gears, which serve to transmit torque between different axes of rotation. The transmission of torque is by positive engagement of the teeth. Accordingly, the tooth itself needs to be designed for strength. The design of gear teeth is a subject that is normally not covered by MBD simulation. MBD analysis can help calculate the tooth-loads, and these loads can then be used as input for a stress analysis program – usually using Finite Element Analysis.

The other main class of problems deals with the design of the gear train itself. Gear trains range from the aptly named simple gear trains to the amazingly complex epicyclic gear trains. In these cases, analyzing the motion of the output shaft and calculating the ratio of input and output torques are the main areas of interest.

The images of a 4-bar mechanism with two gears (on the right), taken from an animation at the KMODDL, (Kinematic Model for Design Digital Library; http://kmoddl.library.cornell.edu/) illustrate how complex the motion can be.

Calculating the efficiency of the gear train is an important but tedious task even for gears whose axes of rotation are fixed, like the worm-driven helicalrack- and-pinion shown below.

Gear models in MBD are relatively easy to build. Revolute joints define the axes of rotation of the shafts, while the gear joint represents the constraint between the two revolute joints.

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5.5 Overview On Different Joint Definitions · 2016. 3. 25. · 3 DOF – 1 algebraic constraint = 2 DOF Thus, there are two degrees-of-freedom in this system, and any two will prescribe