Kinetostatic Force Analysis:

Force analysis at joints when a motion is imposed on a kinematic-chain, when the Parts that have Mass and Mass Moment of Inertia. Spring and pseudo-friction forces can also be imposed on the kinematic-chain.

Dynamic Analysis :

Motion and force analysis of the vibrational response of a kinematic-chain in response to a motion imposed on a kinematic-chain, when the Parts that have Mass and Mass Moment of Inertia, Stiffness, and there is Backlash and Damping at joints.

Mass Properties :

The term we use for Mass, Mass Moment of Inertia and the location of the center-of-mass. Units of Mass Moment of Inertia are

Stiffness :

The Force that you need to deflect a part by a millimeter . Units of Stiffness are .

Rigidity :

The Torque that you need to deflect a part by a radian . Units of Stiffness are .

Backlash :

The millimeters or degrees that you can move the output (tooling) without moving the input (Follower). Units of Backlash are or ( ).

Damping :

The Force that opposes the velocity and is proportional to the velocity. Units of Damping are .

Critical Damping :

The minimum amount of viscous damping that results in a displaced system returning to its original position without oscillation.

Damped Natural Frequency :

In the presence of damping, the frequency at which the system vibrates when disturbed.

Damped Natural Frequency is less than undamped natural frequency.

Damping Ratio :

A ratio that characterizes how the vibrational response attenuates, or decays, over time. If zero, the response of the model continues to oscillate around the command motion without any decay. If it is between 0 and 1, the response will overshoot the motion-command and oscillate around the command, but the overshoot attenuates with time. If greater than 1, the response will always lag the motion-command and not overshoot the command. If equal to one, the response is 'critical', in that it does not overshoot, but if the ratio is any less, the response will overshoot.

Generalized Force :

A term that implies Force and/or Torque.

Inertia Coefficients / Torque Coefficient

The Inertia Coefficients indicate the inertia values that are reflected to the Motion-Part of the kinematic-chain at each step in the machine-cycle. There are three Inertia Coefficients. They relate to Acceleration, Velocity Squared, and Gravitational Inertia-Coefficient.

The three Torque Coefficients indicate the Torque that is required to overcome the Inertia, Velocity-Squared, and Gravitational Inertia coefficients at each step in the machine-cycle.

Add and use the Dynamics-Briefcase FB as a container for a Spring-Damper FB and a Inertia FB.

The Dynamics Briefcase FB is the 'gateway' from the kinematic model to the Function-Blocks that do the Dynamic-Analysis.

Input-Connector

It has one input-connector.

You connect to its input-connector a wire from the output-connector of a Motion-Dimension FB*.

The Motion-Dimension FB controls the motion of a degree-of-freedom in a kinematic-chain.

The label at the input-connector is .

The input is the motion-command, , which is the input to the Dynamic Analysis.

The input is the motion axis whose dynamic response you want to analyze.

* You must also connect the wires of Function-Blocks in the kinematic model in a particular way - see example, later.

Output-Connector

It has one output-connector, .

The data at the output-connect is the same kinematic motion data at its input-connector.

Dynamics-Briefcase FB and parameters.

Edit the Dynamics Briefcase FB to add/remove input-connectors, the other Dynamic FBs, to control the integration parameters and the parameters for the Graph FB.

Add the Spring-Damper FB to the graphics-area and then to the Dynamics-Briefcase FB.

The Spring-Damper FB subtracts the motion-response from the motion-command to calculate the motion-error. From the motion-error it calculates the generalized Force (Torque or Force) that drives the model.

There are two input-connectors and three output-connectors.

Input-Connectors

Top : connect a wire from the output-connector of the Dynamics-Briefcase FB to this input-connector

Bottom : from the output of a Inertia FB. It is the dynamic motion-response,

Output-Connectors

Top : the positive value of Generalized Force that we calculate from the two motion inputs.

Middle : the negative of the Generalized Force.

Bottom : equal to the motion-command at the Top input-connector - typically connect as one input to the Graph FB.

Spring-Damper dialog and Parameters

Edit the Spring-Damper to enter the Stiffness and Backlash parameters in the Spring-Damper dialog.

See Spring-Damper FB

Add the Dynamic-Inertia FB to the graphics-area and then to the Dynamics-Briefcase FB.

The Dynamic-Inertia FB calculates the motion-response from the Generalized Force.

There are three input-connectors and three output-connectors.

Input-Connectors

Top: the Generalized Force - connect a wire from the Top output-connector of the Spring-Damper FB -

Middle: not used

Bottom: not used

Output-Connectors

Top: the motion-response -  in response to the Generalized Force, at its input.

Middle: the negative of the motion-response - which we connect to the Bottom Input of the Spring-Damper FB.

Bottom: not used

Dynamics-Inertia dialog and Parameters

To calculate the motion-response, the Dynamic-Inertia FB calculates what we call the Inertia Coefficients over a machine-cycle - Gravity, Velocity Squared, and Acceleration coefficients - see Inertia Coefficients tab.

For each Inertia Coefficient there is a so-called Torque Contribution over a machine -cycle - Gravity Torque, Velocity Squared Torque, and Acceleration Torque - see Torque Contribution tab.

See Dynamics-Inertia dialog

Add a Graph FB from the Kinematic FB menu or toolbar.

It has the four input-connectors for four different plots. The bottom input-connector that you usually use for the X-axis is not usually used.