Linkage synthesis is designing a linkage to meet a desired output.  Since most linkages are capable of complex motion, this has been a daunting task except for specific linkages with predictable motion.  In this article we will look at various types of linkage synthesis. Before getting to far, we need to define the term “precision …

## Slider Crank Inversions

The slider crank is a very common linkage that is found in a variety of machines.  The most recognizable version of the slider crank is found in an engine in the form of a crank shaft, connecting rod, piston, and cylinder.  This mechanism also comes in different forms called slider crank inversions. The slider crank …

## Monte Carlo Integration

This video shows how definite integrals can be estimated using Monte Carlo simulation.  A triple integral is estimated using Simulation Master. Other Resources Blog article on Monte Carlo integration. Tutorial on using the Simulation Master integration tool.   For more videos, visit our YouTube channel. Excel is a registered trademark of Microsoft Corporation.  Used with permission …

## Hydraulic Cylinder Calculations

Hydraulic cylinders are the muscle of a hydraulic system.  In this article we’ll present the equations for hydraulic cylinder calculations and discuss efficiency. Cylinder Equations – SI These are the formulas for SI units.  All formulas are for theoretical values. Cylinder Equations – US These are the formulas for US units.  All formulas are for …

## Correlation Matrix Definiteness

When simulating a model, some random variable inputs may be correlated.  One way to introduce this correlation into the simulation is by rank order correlation.  In this method a correlation matrix is used to define the correlation structure.  The correlation matrix definiteness is important. A correlation matrix must be either positive definite (PD) or positive …

## Hydraulic Pump Calculations

Hydraulic pumps are the heart of a hydraulic system.  In this article we’ll present the equations for hydraulic pump calculations and explore efficiencies. We’ll start with the equations in SI and US units. Pump Equations – SI Pump Equations – US Hydraulic Pump Efficiencies There are three types of efficiency associated with a hydraulic pump. …

## Hydraulic Motor Calculations

In this article we’ll dive into hydraulic motor calculations and the important topic of efficiency.  Many hydraulic calculators ignore efficiency altogether and merely calculate theoretical values with 100% efficiency.  Manufacturers typically don’t get too deep into efficiency either. First we’ll present the equations for various parameters of a hydraulic motor in both SI and US …

## Planetary Gear Train Analysis

The planetary gear train is an important, but complex mechanism.  When it comes to analyzing rotation directions and gear speeds, intuition is not enough.  We’ll look at the superposition method to determine speeds and rotation directions. For a planetary (a.k.a. epicyclic) gear train there are three possible inputs/outputs: two gears and the planetary gear carrier.  …

## Spiral Bevel Gear Forces

In this article we’ll look at spiral bevel gear forces that result from gear mesh. These forces are important to determine the loads on shafts and bearings. Spiral bevel gears are useful when input and output shafts are not parallel. Most often, spiral bevel gear shafts are 90 degrees apart. Anatomy of a Bevel Gear …

## Straight Bevel Gear Forces

In this article we’ll look at straight bevel gear forces that result from gear mesh. These forces are important to determine the loads on shafts and bearings.  Straight bevel gears are useful when input and output shafts are not parallel.  Most often, straight bevel  gear shafts are 90 degrees apart. Anatomy of a Bevel Gear …