﻿ Casyopee - Modelling with respect to an angle
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## Connecting rod and crank mechanism

Consider M a mobile point on the circle centred in o with radius one and P the point on the half-line [ox) such as MP is constant (equal to a, a being a positive parameter). We want to model the dependency between the distance oP and the position of M over the circle. For mechanics, [oM]  is part of the crank and [MP] is the connecting rod.

101 - Connecting rod and crank mechanism

Follow the construction in the NotePad Figure 101. You may assign a speed to point M in order to animate the mechanism (see p. 11). Stop by Action Stop Mobile Points.

To model the mechanism, OP is obviously the dependent variable to choose. But, what might we choose an independent variable? We can create the angle between the x-axis and OM that varies while M is moving on the circle.  Click the angle button  and then a point on the axis (choosing fixed point in the menu), O and M.

Figure 102 - Creating calculations (distance and angle)

Figure 103 - domain and formula of the model function

After asking Casyopée to compute the function by way of the model menu, you evaluate the domain and confirm (OK). If you asked to check existence, you get a message warning that Maxima cannot guaranty that the definition is mathematically correct.

Figure 104 - Casyopée's warning

Note that such warning can happen whereas the definition is correct; it is because of symbolic computation limits. That is why you can ignore the warning. After a new warning the function can be created.

Figure 105 - Rod and crank, model function

Note also that the reverse dependency (c0 -> c1) does not work because for one value of OP correspond two values of the angle. The diagnostic will be: The calculation depends on M. Casyopée cannot compute a model function with the independent variable c0.

## Connecting rod and crank mechanism

Consider M a mobile point on the circle centred in o with radius one and P the point on the half-line [ox) such as MP is constant (equal to a, a being a positive parameter). We want to model the dependency between the distance oP and the position of M over the circle. For mechanics, [oM]  is part of the crank and [MP] is the connecting rod.

101 - Connecting rod and crank mechanism

Follow the construction in the NotePad Figure 101. You may assign a speed to point M in order to animate the mechanism (see p. 11). Stop by Action Stop Mobile Points.

To model the mechanism, OP is obviously the dependent variable to choose. But, what might we choose an independent variable? We can create the angle between the x-axis and OM that varies while M is moving on the circle.  Click the angle button  and then a point on the axis (choosing fixed point in the menu), O and M.

Figure 102 - Creating calculations (distance and angle)

Figure 103 - domain and formula of the model function

After asking Casyopée to compute the function by way of the model menu, you evaluate the domain and confirm (OK). If you asked to check existence, you get a message warning that Maxima cannot guaranty that the definition is mathematically correct.

Figure 104 - Casyopée's warning

Note that such warning can happen whereas the definition is correct; it is because of symbolic computation limits. That is why you can ignore the warning. After a new warning the function can be created.

Figure 105 - Rod and crank, model function

Note also that the reverse dependency (c0 -> c1) does not work because for one value of OP correspond two values of the angle. The diagnostic will be: The calculation depends on M. Casyopée cannot compute a model function with the independent variable c0.

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## Connecting rod and crank mechanism

Consider M a mobile point on the circle centred in o with radius one and P the point on the half-line [ox) such as MP is constant (equal to a, a being a positive parameter). We want to model the dependency between the distance oP and the position of M over the circle. For mechanics, [oM]  is part of the crank and [MP] is the connecting rod.

101 - Connecting rod and crank mechanism

Follow the construction in the NotePad Figure 101. You may assign a speed to point M in order to animate the mechanism (see p. 11). Stop by Action Stop Mobile Points.

To model the mechanism, OP is obviously the dependent variable to choose. But, what might we choose an independent variable? We can create the angle between the x-axis and OM that varies while M is moving on the circle.  Click the angle button  and then a point on the axis (choosing fixed point in the menu), O and M.

Figure 102 - Creating calculations (distance and angle)

Figure 103 - domain and formula of the model function

After asking Casyopée to compute the function by way of the model menu, you evaluate the domain and confirm (OK). If you asked to check existence, you get a message warning that Maxima cannot guaranty that the definition is mathematically correct.

Figure 104 - Casyopée's warning

Note that such warning can happen whereas the definition is correct; it is because of symbolic computation limits. That is why you can ignore the warning. After a new warning the function can be created.

Figure 105 - Rod and crank, model function

Note also that the reverse dependency (c0 -> c1) does not work because for one value of OP correspond two values of the angle. The diagnostic will be: The calculation depends on M. Casyopée cannot compute a model function with the independent variable c0.

Creation date : 06/10/2014 - 16h14
Category : - help