What is SAM ?
SAM (Synthesis and Analysis of Mechanisms) is an interactive PC-software package for the design, analysis (motion and force) and optimization of arbitrary planar mechanisms. Mechanisms can either be generated via the design wizards or they can be assembled from basic components including beams, sliders, gears, belts, springs, dampers and friction elements. SAM integrates pre-processing, numerical analysis and post processing, such as animation and xy-plots, in an easy to-use environment offering pull-down menus, mouse support and help facilities.
The mathematical foundation of the analysis kernel, which is inspired by the well-known finite element approach, offers a large number of features and overcomes many of the problems of traditional mechanism programs. Open loop, closed loop, multiple loop and even complex planetary mechanisms can equally well be analyzed due to the finite element formulation. Even the most complex mechanisms, including planetary gear trains, can be modeled within minutes.
SAM offers a set of design wizards which will help you to synthesize mechanisms for specific tasks, such as :
In case these design wizards do not provide the solution to the specific design problem, the user has to rely on his experience, previous design, handbooks or trial&error to invent the mechanism, which can then be modelled and analyzed in SAM.
- Angle function generation (a minimum of 3 pairs of input/output angles are to be satisfied).
- 3-Position/angle synthesis of the coupler plane
- Approximated straight line motion
- Exact straigh line motion
SAM is equipped with a large library of basic elements, including :
which allows the analysis of a huge variety of mechanisms. The unique mathematical foundation of the program offers a large number of features and overcomes many of the problems of traditional mechanism programs. Open loop, closed loop and even multiple loop mechanisms are treated in the same way and even the most complex mechanisms, including planetary gear trains, can be modeled within minutes.
- beam, slider
- belt, gear
- spring, damper and friction element (both translational and rotational)
- non-linear spring
SAM allows the definition of multiple inputs, which can either be defined in terms of absolute displacements or in terms of elemental change of shape to model relative inputs (e.g. elongation of a hydraulic cylinder or relative rotation of a robot elbow). Each of the inputs can be defined independently. Various frequently used input motion laws, such as
are available and can be combined to form any desired input diagram. Inputs can also be read from an external ASCII file or defined via a table to enable the definition of arbitrary motions. This latter feature is especially handy for the modeling of non-standard cam profiles.
- constant velocity
- cyclical motion
- 2.order velocity profile
- cubic splines
The DXF import/export facility lets you export your conceptual mechanism design to any CAD program to work out the details and it lets you import CAD data to easily set-up the mechanism in SAM or to perform animation of the final mechanism.
Once the mechanism has been constructed and the inputs have been defined any of the following kinematic quantities can be calculated (all relative or absolute) :
Furthermore SAM can perform force-analysis, thus enabling the calculation of :
- nodal position, displacement, velocity, acceleration
- angles, angular velocity and acceleration
- driving torque (force)
- reaction forces in bearings
- internal forces in elements
- required or transmitted power
The analysis results can be displayed either in tabular or graphical form. The tabular listing can be viewed on the screen, send to a printer or stored in a readable formatted list file. The x/y plot option allows to plot any variable against time or any other variable. An unlimited number of functions can be combined into one x/y plot with optionally two different scalings to allow proper multiple display of variables with different amplitude ranges. It is possible to output selected data to an external file (ASCII format) for customized post-processing.
SAM can also animate the mechanism motion.. As a further aid for the designer the path and velocity hodograph of any number of moving points can be plotted. Also, a complete project documentation (ASCII-format) can be automatically generated.
Optimization (Professional version of SAM only !)
The optimization module of SAM offers single-function multi-parameter unconstrained optimization based on a mix of evolutionary algorithms and Simplex techniques.
Taking the initial design/topology as a starting point one can for example further improve the quality in which the trajectory of a coupler point equals the target trajectory by changing the geometry of the mechanism within pre-defined ranges. Or one can minimize the peak or RMS value of the driving torque of a mechanism by adding a compensating mass and let SAM determine the optimal value of the mass and its position within the allowable range. Just as in the case of the trajectory optimization one can also specify a reference function and minimize the difference between the actual and the reference function. When designing for example fitness equipment one is generally seeking a predefined force as function of displacement.
The goal for optimization can be the minimization or maximization of a variety of properties (peak, RMS, average, ...) or the difference between the actual and the target behaviour of a mechanism, such as :
SAM seeks the optimum by modifying the following properties within user-defined ranges :
- Trajectory of a node (with of without prescribed timing)
- Any motion or force quantity (as function of time or another quantity)
The optimization process in SAM is based on a two step approach, consisting of :
- geometry of mechanism
- element properties, such mass, spring constant, transmission ratio, ...
- Exploration of the design space
- Optimization of a specific solution