Kinetostatic Forces
A Kinetostatic Analysis calculates the resultant forces1 at joints from the motion that is imposed on the mechanism by an 'idealised power source2. MechDesigner will do the Kinetostatic-Analysis of each kinematic-chain on a Mechanism-Plane.
A Dynamic Analysis is the opposite. It calculates the resultant motions of the mechanism from a force or torque that is imposed on the mechanism. MechDesigner does not do a 'dynamic-analysis'.
Notes:
1: 'Force': when we use the word 'force', it will refer to a 'generalised force', which will include 'moments'.
1: Other 'schools' call these Dynamic-Forces. See Dynamic Forces.
2: An Idealised Power Source [also Fictitious Power Source] has an infinite capacity to move the parts exactly as given by the planned motion. A simple example of an 'Idealized Power Source' would be a cam-shaft that does not deviate from constant velocity even though the torque required to drive the cam-shaft is changing rapidly.
Kinetostatic-Forces:
| • | Reaction forces at joints |
| • | Reaction forces at anchor points of Springs |
| • | Reaction forces at the contact point between gear teeth flanks, and between a cam-profile and cam-follower. |
| • | The 'Motive Force' to move each kinematic-chain with a predefined motion. |
Kinetostatic-Forces are a function of:
| • | The Motion of Parts: Inertia force, Centripetal force, Coriolis force. We assume the motions of all Parts move exactly as planned. |
| • | The Mass distribution: Centre-of-Mass, Inertia |
| • | External Forces: Spring, Drag, Coulomb Forces |
| • | Gravitational Force – when the is not horizontal |
Kinetostatic-Forces do not include:
| • | Forces that result from impact between colliding Parts |
| • | Forces from the impact after traversal of backlash in Joints, Gear-Pairs or Cam-Tracks. |
| • | Forces from friction at Joints. |
| • | Forces from magnetism, electricity. |
| • | Forces in kinematic-chains that are not |
| • | Forces that are not on the – all forces are made to be coplanar with the |
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Kinetostatic-Forces are for 'Ideal' Kinematic-Chains:
IDEAL KINEMATIC-CHAINS:
| • | Rigid Parts do not bend, twist or stretch |
| • | Rigid Parts do not expand with temperature |
| • | Joints do not have play (backlash) |
| • | Joints do not have Friction |
| • | All Parts follow the motion design exactly |
| • | The Power Source moves exactly as planned |
| • | Contact surfaces at Cams and Gears do not deflect |
| • | The kinematic-chain is 100% efficient |
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REAL KINEMATIC-CHAINS:
| • | Real Parts do deflect, twist and stretch |
| • | Rigid Parts do expand with temperature |
| • | Real Joints do have backlash, play |
| • | Real Joints do have friction between each Parts. |
| • | Real Parts do not move exactly as planned |
| • | Real Motors do not move exactly as planned |
| • | Real contact surfaces do deflect |
| • | Real kinematic-chains are not 100% efficient. |
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You may think what is the point in doing a model, because it will deviate from the Real Kinematic-Chain by so much! However,
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Configure the Power Source.
It is important that you Configure the Power Source correctly for each kinematic-chain before you analyse forces.
That is, you must select from which joint [or cam, or spring, or gear] each kinematic-chain gets its 'power'.
Note: The Moment Vector we show at a joint is the Torque a Servomotor needs to provide to the mechanism. When you add a Servomotor and Gearbox, you must also accelerate their inertias, and overcome their friction. To find the Servomotor and Gearbox combination for your application, see Kinetostatic Motor Torque and Speed Data.
In MechDesigner, each kinematic-chain has three different possible sources of 'Power':
A Motor
If you drive a kinematic-chain with a motor (rotary or linear), make sure the Power Source is given to the correct joint.
By default, MechDesigner gives the Motor to the joint with the .
However, it is possible, especially when you use inverse-kinematics, that the Motor drives a different joint.
A 2D-Cam
Usually, a cam is a child to a Part in one kinematic-chain, and the cam-follower is a child to a Part in a different kinematic-chain. In the default case, when you use Display Forces, you will see two motors: one motor to drive each kinematic-chain.
However, the cam is most often the cam-follower's Power Source and not a motor. Hence, you must Configure the Power Source of the motor that drives the cam-follower's kinematic-chain so that its Power-Source is the cam. The remaining motor drives the cam.
A 'Spring' that acts as a Linear Motor
When you add a Spring Force FB between two Points in a kinematic-chain, or different kinematic-chains, it simply exerts a Force. However, it can be a Linear Motor. You must configure the power source to make the Spring Force FB the Power Source.
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The Torque and Force values at each joint are a function of the joint you select for the Power Source.
To illustrate this, we model a four-bar kinematic-chain, arranged as a simple a mechanism [see images below]. The angle between each part is 90º. [See the images below]. The Mechanism is stationary.
The four-bar includes:
This is a Rocker. It is the vertical Part on the left.
The Rocker has a 1kg mass that is 100mm horizontally to the left of the Pin-Joint made with the Base-Part. Its weight is ~9.81N [1kg * 9.81m/s/s=9.81N].
There are two Parts: one horizontal, the other vertical and parallel to the Rocker, on the right.
The position of the mass does not change when we move the Power Source from the left to the right.
However, when we move the Power-Source, the resultant Forces at each Joint are completely different.
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 Simple Mechanism : Power Source at Bottom-Left Joint. |
Configure Power Source 1
If we put the Power Source at the Pin-Joint on the left, near to the Mass .
Resolve Forces:
| • | A vertical Force acts at the Pin-Joint of the Rocker of 9.81N, because of the weight of the mass |
| • | No other Forces at the other Joints. The other Parts are massless. Thus, in this case, they do not need to resist a force. |
Resolve Moments:
| • | 0.98Nm Torque that acts at Pin-Joint of the Rocker. We need the torque to balance the Moment of 9.81Nm from the 1kg mass, that is 0.1m horizontal, |
We can imagine that the Drive Torque keeps the Rocker in its vertical position.
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 Simple Mechanism : Power Source at Bottom-Right Joint |
Configure Power Source 2
If we put the Power Source at the right Pin-Joint. The Mass does not change from Option 1.
Resolve Forces:
| • | Vertically and horizontally to give forces at the Pin-Joints. |
| • | The force due to the mass is transmitted through the kinematic-chain to the motor. The motor holds the mass in position. |
Resolve Moments:
| • | Resolve Moments gives the same Moment (Torque), but at the Pin-Joint on the right. |
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Example 'Configure the Power Source'