Planar Linkages


Drives and Guides
Dual Linkages
Sensors

Description:

The models of this library combine links, bodies and joints. Therefore, they represent ready-to-use drive or linkage systems. Furthermore, these models can be parametrized by simple geometric and mass data and they provide typical result quantities for the analysis and synthesis of linkages. Hence, this library contains elements for a very efficient modeling of linkage mechanisms.
Every planar linkage can be created by combinations of Drives and Guides and Dual Linkages. Finally, also the Sensors help to analyze and synthesize such systems.

Further general sub-chapters


General Modeling Basics

Example (small tutorial): Modeling of a quadrilateral linkage (four-bar linkage) with four revolute joints

  1. Open a new model in SimulationX and insert a Rotary Drive element from Drives and Guides (-> element drive1) and a Dual Linkage with 3 Revolute Joints (RRR) from Dual Linkages (-> element rRR1)
  2. Connect ctrP of drive1 with ctr1 of rRR1 (see figure 1)

    Figure 1: Connect two basic elements
  3. For element drive1, set the color to green (dialog tab Visualization, parameter color={0,0.6,0})
  4. Open a new 3D View (see figure 2):

    Figure 2: 3D view of the quadrilateral linkage
  5. Ready => Run simulation ...

Further and more complex examples (samples) can be found via the Sample Browser: Go to folder "Power Transmission (2D, planar)" and sub-folder "Planar Linkages";
or: select a type or package in the library bar, click right, select "Samples...".

About the connectors

The elements have three general kind of connectors (see figure 3):

  • Independent 2D-Connectors
  • Dependent 2D-Connectors
  • 1D-mechanical connectors

Figure 3: Kind of connectors at a basic linkage element (here RRR)

Independent 2D-Connectors:
They represent the fixed part of an "input" joint. The input joint can be fixed at the environment or at another linkage (body), if it is connected to an dependent 2D connector.
The independent connectors have the same meaning as all 2D-Connectors of the Planar Mechanics world. They correspond to pin point frames (PCS) and the are linked with the position and orientation parameters and results (x10, y10, etc.; see chapter Basics and General Information of Planar Mechanics).
Independent 2D-connectors can be identified by their names: "ctr" + count number; e.g. ctr1 and ctr2 in figure 3).
Independent 2D-connectors can also be identified by their graphical representation in the 3D view as joint. If they are fixed at the environment they will be represented by black & white cylinders (revolute joints) or black cubes (prismatic joints) (see figure 4).


Figure 4: 3D view of independent 2D-connectors (fixed joint parts, fixed to environment)

Hint: Independent joint parts will change their 3D representation, when they will be connected to an element.

Dependent 2D-Connectors:
They represent the link. Here, further elements for moving bodies or independent 2D-Connectors of other linkages can be connected.
Note: The linkage elements, represent the link inside. Within a linkage model the link can always move. Thus, a 2D-connection at a dependent 2D-connector shows no initial value parameters (initial values and the link motion will be computed by the linkage element). So, that' the reason, why its called "dependent" connector. The motion of further structures depend on the linkage element.
Hint: Dependent connectors represent also a pin point frame (PCS), but this can be neglected here. So, there are also no parameters or result quantities corresponding to this.
Dependent 2D-connectors can be identified by their names: "ctr" + "L"/"P" + count number; e.g. ctrL1 and ctrL2 in figure 3 or ctrP in figure 1).

1D-mechanical Connectors:
These connectors can be used for the connection of 1D-mechanical sub-systems (linear or rotational) to represent drives or loads. These connectors act as interfaces to the libraries Rotational Mechanics, Linear Mechanics or Power Transmission (1D).
1D-mechanical connectors can be identified by a black dot and a red arrow in the diagram view and by their names: "ctr" + "R" (for rotation) or "T" (for translation) + "L" (if it is connected to an internal link) + count number; e.g. ctrRL2 and ctrR2 in figure 3).

Visualization of linkages in the 3D View

All elements of this library support their visualization in the 3D view. This section describes the measurements of the 3D primitives and the corresponding parameters. More information about the visualization will follow in the next chapters. Note: The additional geometry parameters will never effect the physical behavior.

The following figure 5 shows a sketch of link body with revolute joint and its measurements.


Figure 5: Link body with revolute joint and measurements

The blue measurements in figure 5 are available as parameters. But not all measurements are available as parameters. In these cases the following internal approaches will be used:

  • inner diameter of a revolute joint: dJi = 0.75*dJ
  • height of a revolute joint ring: hJo = 0.5*hJ
  • outer diameter of a revolute joint pin, if not available as parameter: dP = 0.49*dJ
  • height of the inner pin of revolute joint, if not available as parameter: hP = 0.9*hJ

For link bodies with sliders, there are the following measurements, shown in figure 6:


Figure 6: Link body with prismatic joint and measurements (lG only if required)