# Clamping Mechanism

High tonnage machines, such as is proposed, cannot operate with a simple in-line hydraulic cylinder, so a toggle mechanism is used.

The most efficient and reliable is the 5 point double toggle.

![Photo](./clamping-mech-photo.jpg)

## 5 point double toggle mechanism

![Toggle clamp iso](./Construction-of-Clamping-Unit.jpg)

The 5 point double toggle mechanism is used on high-tonnage machines

[Video -Toggle Clamp Mechanism](https://www.youtube.com/watch?v=w0k1a_s6GWk)

![Toggle clamp diagram](./clamping.gif)

## Design of a clamping mechanism

The challenge of designing a high tonnage toggle clamp is to be able to calculate the ratio of input and output forces. This is called the Mechanical Advantage. This ratio allows an appropriate hydraulic cylinder and power supply to be selected.

The geometry of the 5 point clamping mechanism is complex, but can be represented algebraically.

Mathematical modelling is discussed in the key paper, [Study on improvements of the five-point double-toggle mould clamping mechanism (2004)](http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.828.9042&rep=rep1&type=pdf)


In a subsequent study, [Key design parameters and optimal design of a five-point double-toggle clamping mechanism (2011) ](https://doi.org/10.1016/j.apm.2011.03.001), an optimization approach is suggested:

In order to calculate optimum link lengths between the 5 points, the algebraic relationship may be subjected to a genetic algorithm in order to rapidly determine the most efficient link geometry for a given set of input values including clamping force and mould opening stroke.

The paper outlines the flow of a machine learning algorithm which can achieve this objective. Injection machine manufacturers appear to develop their own applications of this approach and their optimization algorithms are not in the public domain.


The algebraic relationship is very clearly laid out in the [Kinematic calculation analysis of micro injection molding machine with double-toggle clamping mechanism based on MATLAB (2012)](http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.876.19&rep=rep1&type=pdf) 

![Clamping mechanism](./double-toggle-clamping-mechanism.png)


![Geometric diagram](./geometrical-drawing-main.png)


The geometric model of double-toggle clamping mechanism

L1----length of back toggle

L2----length of frontal rod

L3----length of larger connecting toggle

L4----length of nether connecting rod

L5----length of middle connecting rod

L6----length of crosshead connecting rod

α ----toggle angle

φ----coping angle

β----angle between L2 and horizontal line

H----height of crosshead center

h----height of template center

γ0----fastigiated angle

θ----angle between L1 and L3

φ0----maximal coping angle

S0----stroke of crosshead

Sb----stroke of moving platen

λ1----ratio of L1 and L2

λ2----ratio of L3 and L4

# Key Formulas:

## Stroke Ratio

![Stroke ratio calcs](./stroke-ratio-calcs.png)

## Velocity Ratio

![Velocity ratio calcs](./velocity-ratio-calcs.png)

## Amplified Force Ratio

![Amplified force ratio calcs](./amplified-force-ratio-calcs.png)

# Machine Learning algorithms
  
  Determining combinations of link lengths in a toggle system is an example of a [Multi-Objective Problem](https://www.youtube.com/watch?v=56JOMkPvoKs)
  
As proposed in the first paper cited above, determining optimal geometry might be achieved using a [Genetic Algorithm](https://en.wikipedia.org/wiki/Genetic_algorithm)
  
  [Video- Genetic Algorithms (full lecture)](https://www.youtube.com/watch?v=lpD38NxTOnk)
  
  This method will produce an optimal design through a mathematical process of evolution. This involves 'breeding' and testing large numbers of configuations of the defined variables (link lengths, in this case), requiring a large amount of computing power, but a tiny fraction of what would be require to attempt to test *all* possible confgurations ('brute force'). Machine learning has been demonstrated to be extremely effective in solving this type of complex problem involving multiple variables.
  
  [Proposal for a visualization and optimization tool in Python](./optimize/ReadMe.md)