"Joint" is a new computer program for the position analysis of arbitrary spatial mechanisms (an arbitrary number of elements and multiple kinematic loops).
It is used to model mechanisms and analyze their mobility (possible positions).
The combination of a powerful computation algorithm and an user-friendly interface makes the program extraordinarily flexible and efficient. The program is a universal and powerful tool for researchers, mechanical engineers and students. It is available as a FREEWARE on a ftp server (http://fmechds01.tu-graz.ac.at/).
"Joint" supports various types of joints as well as other elements of mechanisms. The provided "User defined" joint allows simulation of an arbitrary relative motion between the connected bodies. Moreover, electronic or mechanical control devices applied to mechanisms can be simulated with the help of the "Control" elements (i.e. robot manipulators).
In the case of one or more kinematic loops, the special algorithm fully automatically attempts to find all possible assembly modes and the corresponding input/output relations if the mechanism is mobile. A robust numerical iteration algorithm allows computation of very complex kinematic systems of an arbitrary configuration and size.
"Joint" also supports an user interface which is based on the windows and menus. The user interface is easy to understand yet very powerful. The topology of a mechanism is determined graphically in a window by using special tools and graphic objects. The parameters of a mechanism are defined in special input dialog boxes. Moreover, the implemented parser allows definition of mechanism's parameters by complicated mathematical expressions.
The computed data can be displayed in diagrams (input/output curves, position coordinates etc... ).
In addition, the computed data can also be exported by using a universal export editor where the format of the exported text file can be specified. This is very useful if the computed data has to be processed by some other application (spread-sheet, rendering, etc.).
Joint has been extensively used in research at "Institut fuer Mechanik, TU-Graz" and it was presented at the "Ninth World Conference on Machines and Mechanisms" in Milano.
(See also the "Introduction" Quick-Time movie.)
If there are any comments or suggestions contact Pavlin Gregor (e-mail: pavlin@fmechds01.tu-graz.ac.at).
II. Installation
Joint runs on any Macintosh® computer (Mac II and later). Application itself requires at least 7 MB of RAM and 3.2 MB of disk space. It is recommended to increase the partition size when working with large files (kinematic chains with many elements). The best performance is achieved with the 68040 processor.
The software is installed by simply dragging the application symbol (icon) from the floppy disk to the desired (arbitrary) folder on your Macintosh.
III. Using the software
This program supports an user interface which enables via windows, menus and graphic elements an organized and simple formulation of an arbitrary kinematic system, an easy control of the computation and a clear representation of the computed data.
III.1. Starting the program
- double click the icon of the application.
- double click the icon of any file which has been created by this program.
- drag an icon of any file which has been created by this program to the icon of the program.
III.2. Elements of the user interface
III.2.1. “Project Window”
Each examined mechanism is associated with its “Project Window” which represents the main component of the user interface. It is possible to open more than just one “Project Window” at the same time. However, various commands, tools and computation procedures can be used for the currently active window and the corresponding kinematic system only. The most important parts of a “Project Window” are:
- “Worksheet”
where graphic elements which represent various elements of kinematic systems, diagrams and text elements can be generated and displayed. These graphic elements can be, like in the common graphic editors, selected and dragged to any position on the “Worksheet”. Moreover, the selected elements can be copied, pasted and duplicated by using the “duplicate” command or deleted by pressing the Delete key. The size of the “Worksheet” can be specified by the user and any of its regions can be accessed by using the scroll-bars if it is larger than the “Project Window”.
- “Tools Palette”.
A tool is activated by clicking the field with its symbol in the “Tools Palette”. After a tool has been selected, the shape of the cursor in the “Worksheet” is changed appropriately indicating the currently active tool.
The “Tools Palette” is divided into two main sections. Its first section contains tools for manipulation on various graphic objects and data displayed in the “Worksheet”. The most important tools:
- “Selector Tool”. It is used to select and drag graphic objects on the “Worksheet” and to activate input dialog boxes of structural or control elements.
- “Connecting Tool”. With this tool a body or a control element (see Graphic Representation of a Kinematic Chain) can be connected to any of the created joints or constraint elements. The “Connecting Tool” doesn’t connect two elements of the same type, and it allows to make only two connections to each joint or constraint element. Furthermore, it doesn’t allow any connections between the control elements and bodies. After selecting the “Connecting Tool”, the actual connection is established in three steps as follows:
1.) Click with the “Connecting Tool” the symbol of one of the elements on the “Worksheet”.
2.) Pull the connection cord from the initially selected element without releasing the mouse button till the second element is targeted.
3.) If the targeted element can be connected to the initially chosen element, it is highlighted and the connection is established as soon as the mouse button is released.
- “Nippers Tool”. It is used to disconnect the connection cords which were created with the “Connecting Tool”. After selecting the “Nippers Tool”, the nippers cursor opens as soon as it is close enough to any cord which can be cut by clicking the mouse button.
The second section of the “Tools Palette” contains the tools for the creation of elements of kinematic networks, diagram elements and text elements.
After selecting a creation tool, a new element is generated by clicking into the “Worksheet” of the “Project Window”.
The creation tools are:
- “Joint Tools”. These tools are used for the creation of all types of joints. For each joint type a specific tool is provided and activated by selecting the appropriate tool field of the “Tools Palette” which is marked with the symbol of the joint.
- “Constraint Element Tools”. These tools are used for the creation of constraint elements.
- Body, Control Element and Diagram tools. They are used for the creation of body, control elements and diagram elements, respectively.
- “Text Tool”. It is used to insert text elements anywhere on the “Worksheet”. By selecting the “Text Tool” and clicking the spot in the “Worksheet”, thus defining the position of the desired text, the dialog box is shown in which the text can be written and various fonts, styles and sizes can be chosen.
III.2.2. Graphical Representation of Structural and Control Elements
Each element of a kinematic system (mechanism) is represented by an icon (symbol) which corresponds to its type. These symbols contain a question mark as long as their element parameters are not defined or necessary connections are missing.
At the bottom of each icon a label with the default element name is attached while on the top the current element number is added. Both, the name label and the current number can be changed by the user in the same way as the file names on the desktop of the Finder® on the Macintosh® computers.
III.2.3. Defining Parameters of Structural and Control Elements
The parameters of a structural or control element are determined in a special input box which is opened either by double clicking the symbol of an element on the “Worksheet” or by choosing command Object Info from the Object Menu. An input box is divided into sections and its configuration depends on the type of a structural or a control element. In the title bar of each input dialog box the name of the current element is shown while its type, corresponding object number and graphic symbol are displayed below the title bar.
The most important part of the input box is the “Parameters section”. It allows either a definition of the general constant geometric parameters (Full parameters), or the Denavit-Hartenberg (DH)parameters. The type of the geometric parameters is chosen by the pop-up menu which is positioned next to the title of the “Parameters section”.
In the case of Full parameters two separated subsections “Body1” and “Body2” are shown in the “Parameters section”. In each subsection a set of vectors a,n, and m describing the position of the joint and the orientation of its axis are determined relative to one of the connected bodies.
At the beginning of the “Body1” subsection, a pop-up menu is displayed which is used to choose one of the connected bodies as the reference body of the vector coordinates defined in this subsection. The name of the remaining body is shown in the title of the “Body2” subsection and automatically defined as the reference body of this subsection. To each body name appearing in the both subsection titles and pop-up menus, the corresponding object number is attached.
In order to simplify the definition of the vectors m (used to measure angle of rotation) and n , it is sufficient to determine vectors m and n which are not parallel and only the direction and orientation of the vector n has to be defined correctly. The coordinates of the vector n and the component of the vector m, which is normal to the vector n, are normalized internally.
In general, parameters can be defined by various mathematical expressions, which can be typed directly into the corresponding editable text fields. These mathematical expressions are checked and evaluated one after another by the parser when the box is closed with the “OK” button. In the case that either the syntax of any expression is not understood by the parser or a run time error has been detected, the box is not closed and the cursor is positioned to the editable field where the problems have been first encountered.
III.2.4. “Math editor”
The expressions of parameters can be defined by using the “Math editor” where all available functions and constants are listed and arbitrary expressions can be defined as well as analyzed. Moreover, also new functions and constants which are specific only to the current joint and used for the definitions of its parameters can be defined in the “Math editor”. In order to open the input box of the “Math editor”, one of the editable text fields has to be first activated and the button “Edit Expression...” has to be clicked.
III.2.5. Diagrams
Diagrams can be created on the “Worksheet” of the “Project Window” by using the Diagram Tool in the same manner as in the case of the structural or control elements. Moreover, they are graphic objects which can be selected, dragged, modified and deleted.
Configuring Diagrams:
The variable parameters, title and scales are defined in a special Diagram Info dialog box. It is opened either by double clicking the diagram element or by choosing the Object Info... command from the Object menu.
III.3. Controlling the Computation
1.) Starting the computation
After the topology of a kinematic chain and its parameters have been determined in the “Project Window”, the computation can be started by choosing the “Run” command from the “Computation” menu. The computation procedure consists of the following consecutive steps:
a.) The kinematic chain is checked in order to find out whether its elements have been defined and connected properly. If there is a problem the computation procedure is aborted and a dialog box with a warning is displayed.
b.) The topology of the examined kinematic chain is analyzed in order to find the optimal reference body (reference frame) and closure conditions in the case of loops.
c.) As next the program attempts to find any possible posture of the examined kinematic chain. (The initial values for the first assembly iteration are obtained randomly.). Note that this procedure is repeated automatically as long as no posture is found.
d.) After the initial posture was found the computation algorithm attempts to find further solutions (possible postures) belonging to the current closure mode. Note that after all possible postures of one mode were found the step "c.)" is automatically repeated until a new posture (a new closure mode) is found.
2.) Stopping and Pausing the computation
The computation can be temporarily stopped by choosing “Pause” and restarted by choosing “Resume” command from the “Computation” menu.
2.) Reseting the computation
By choosing command “Reset” from the “Computation” menu all computed data is destroyed.
