Kinematic Definitions and Elements

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Kinematic Definitions and Elements

Basic Kinematic Elements

You assemble mechanisms (called kinematic-chains, or linkages) with the Parts and Joints - the basic kinematic elements.

Some Basic Definitions

Kinematics and Kinematic-Chains

Kinematics

The study of the relative motion of rigid-bodies that are connected with joints. Kinematics does not consider the forces that you need to move a kinematic-chain.

Kinematic-Chain

A series of rigid-bodies and joints such that all move in a predictable way given the motion of a minimum of one rigid-body. One rigid-body in a kinematic-chain is the Reference Frame - called the Base-Part in MechDesigner.

Rigid Body

A rigid-body is not a real body. It is an ideal-body.

A rigid-body:

•does not stretch

•does not bend

•does not twist

•does not vibrate

•does not expand with heat

•has an exact and specified length

Joint

A Joint allows the relative motion between Rigid-Bodies. It is an ideal-joint.

An ideal-joint:

•does not have backlash

•does not resist the motion with friction or other deleterious force.

•does not have a dimension - other than the location of an axis in an ideal-body.

Machines versus Mechanisms

Machines are those kinematic-chains that do useful work, that transmit forces to transmit power from an input to an output

Mechanisms are those kinematic-chains that transmit motion, or information.

In MechDesigner, there is no distinction. However, there is often a semantic debate as to when a mechanism becomes a machine, and vice versa. The distinction is usually made as the design intent

•Machines transmit force. But they also transmit motion from part to part.

•Mechanisms transmit motion. But they also transmit force from part to part.

Parts

minus        MechDesigner names of Parts

In MechDesigner, we use the name Part for a Rigid-Body.

We use three different names for a Part. Each is a Rigid Body  We give them derived-names to make the instructions in our help easier to follow.

BasePart-Partname

Base-Part.

The small XY-axes are at the Origin and are on the Mechanism-Plane.

You must add at least one joints between it and a different Part. Usually there are more joints.

Before you can add Joints between it and other Parts, you must add sketch-elements to the Base-Part.

AddedPart-Partname

Added-Part - or a Part.

The default Part we add to the model is a kinematically given the term Binary Part. (see below: Kinematic names)

You edit it to make it a Ternary, Quaternary Part. (see below: Kinematic names)

Added-Parts lie on the Mechanism-Plane.

KC-Joint-Ball1

Connecting-Part

We use Connecting-Parts in Spatial kinematic-chains.

Connecting-Parts do not lie on the Mechanism-Plane.

They join two different Parts on two different Mechanism-Planes and between two different Mechanism-Editors.

minus        Kinematic names of Parts

Reference Frame: a Frame of reference to identify the relative motion of moving Parts.

Binary Links, Ternary Links, Quaternary Links... Parts with two, three, four and more Points.

We do not 'add' Binary, Ternary and Quaternary Parts. We edit a Part to add any number of Points.

For completeness, Parts with two, three and four Points are shown below.

BasePart-Partname

Reference Frame

A Reference Frame is a Part that does not move - it is fixed in the Mechanism Plane.

It is a Frame of Reference from which we can specify or measure the motion of moving Parts. The Base-Part may itself move relative to other Mechanism Planes.

KC-Part

Binary Link:

Binary Links have a Point at each end.

This is the default Part in MechDesigner,

KC-Part-Ternary Link

Ternary Link:

A Ternary Part has three Points in it. To make a Ternary Part in MechDesigner:

1.Add a (Binary) Part

2.Edit it in the Part-Editor

3.Add a Point!

4.Close the Part -Editor.

In this image, the extra Point is at the Apex of two Lines.

KC-Part-QuarternaryPart

Quaternary Link

Here is a Quaternary Part. It has four Points.

It can get boring. You guessed it, add Lines, or Points, to give two extra Points.

Similarly, you can add five, six, seven, eight.... Points to a Part.

Joints

Joints constrain Parts to move relative to each other in a predefined way. Different types of joint give different relative motion.

A Joint is also known as a 'Kinematic-Pair'. There are three types of Kinematic-Pairs; each gives a different relative motion.

minus        Lower Kinematic-Pairs

These use Points, Lines and Planes to constrain contact between two Parts with Points, Lines and Planes.

There are six Lower Kinematic Pairs. We have three in MechDesigner.

The other three are: Screw, Cylindrical and Plane on Plane. We do not have these in MechDesigner.

KC-Joint-Pin1

Revolute Pair (a Pin-Joint).

A line (the rotation axis) in a Part stays collinear with a line (the rotation axis) in a different Part.

Planes that are perpendicular(⊥) to the Lines in the Parts stay in contact.

KC-Joint-Slide1

Prismatic Pair (a Slide-Joint)

A Line in a Part stays collinear with a Line in a different Part.

Planes that are parallel to the Lines in the Parts stay in contact.

KC-Joint-Ball1

Spherical Pair (a Ball-Joint)

A Point in a Part stays in contact with a Point in a different Part.

A rule in MechDesigner:

There must be a Ball-Joint at each end of one Part.0

 

minus        Higher Kinematic Pairs

Constrains contact between two Parts with Curves or Surfaces - also called a 'Half-Joint'.

KC-HigherPair-Cam1

Cam and Cam-Roller Pair

A cam-roller stays in continuous contact with a Cam surface.

Gear-PairOption1Ex

Gear-Pair

The contact between the involute curves of gear teeth.

minus        Wrapping Kinematic Pairs

Constrains Points to be in contact with a sketch. It can be used to model belts, chains, and other such devices.

KC-WrappingPair-Belt

Belts

We constrain a Point (called a Motion-Point) to move along a sketch-path with a Motion-Path FB

It is possible to configure the sketch-elements as a loop (sketch-loop), and so make Points follow the continuous loop - as does a Belt.

You can use a sketch-loop to design Belt Paths or Chains Paths.

Motion-Parts and Motion-Dimensions

There are two elements for which we specify a motion.

Motion-Parts: You specify the motion of a Part with motion-values at the input to a Motion-Dimension FB.

Motion-Points: You specify the motion of a Point with motion-values at the input to a Motion-Path FB.
Rocker icon

Rocker icon

Slider icon

Slider icon

The parameter that the Motion-Dimension FB  specifies is:

•Angle between two Parts when we join them with a Pin-Joint. We call the Motion-Part a Rocker

- or -

•Distance between two Parts when we join them with a Slide-Joint. We call the Motion-Part a Slider

Icon-FB-MotionPathMotion-Path icon

The parameter the Motion-Path FB specifies is:

•Distance relative to the start-Point of a sketch-element