Kinetostatic Forces

A Kinetostatic Analysis calculates the resultant forces1 at joints from a 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 Mechanism-Plane is not horizontal
Which joint gives the 'Power' to the kinematic-chain. See: Why Configure the Power Source

Kinetostatic-Forces do not include:

Forces that result from impact between colliding Parts
Forces because of impact after traversal of backlash in Joints, Gear-Pairs or Cam-Tracks.
Forces because of friction at Joints.
Forces because of magnetism, electricity.
Forces in kinematic-chains that are not kinematically-defined chains
Forces that are not on the Mechanism-Plane – all forces are coplanar with the Mechanism-Plane

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

REAL KINEMATIC-CHAINS:

Real Parts do deflect, twist and stretch
Rigid Parts do expand with temperature
Real Joints do have play
Real Joints do have friction
Real Parts are not followed by the motion design exactly
The Motor does not move exactly as planned
Real contact surfaces at Cams and Gears do deflect
Real kinematic-chains are not 100% efficient.

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 tell MechDesigner at 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 inertia, 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 Motion-Dimension FB.

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.  When you use Display Forces, you will see two motors: one motor drives 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 so that the cam-follower's 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.

tog_minus        'Example of Configure the Power Source'

The Torque and Force values at each joint are a function of the joint you select for the Power Source.

We can illustrate this with a simple mechanism

We model a four-bar kinematic-chain, arranged as a simple a parallelogram [see images below]. The angle between each part is 90º. See the images below.

The four-bar includes:

the Motion-Part.

This is a Rocker. It is the vertical Part on the left-side.

The Rocker has a 1kg mass that is 100mm horizontally to the left of the Pin-Joint made with the Base-Part [Local Coordinates in Rocker 0,100]. Its weight is ~9.81N [1kg * 9.81m/s/s=9.81N].

an R-R-R Dyad.

There are two Parts: one horizontal, the other vertical and parallel to the Rocker, on the right-side.


Example

When we configure the power source we nominate which joint, cam, spring or gear that we want to be the 'drive' for the Mechanism.

To illustrate how important it is to nominate the correct Joint, we will Configure the Power Source to be at two different joints in the 'Simple Mechanism' below.

The Mechanism is stationary. There is a Mass to the left Side, which belongs to the vertical Part to the left-side of the mechanism.

The position of the mass does not change when we move the Power Source from the left-side to the right-side.

However, when we move the Power-Source, the resultant Forces at each Joint are completely different.

Cofigure Power Source: Case 1 - Motor at left Grounded Joint

Simple Mechanism : Power Source at Bottom-Left Joint.

Configure Power Source 1

Put the Power Source1s-red at the Pin-Joint on the left, near to the Mass2s.

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.

Cofigure Power Source: Case 1 - Motor at right Grounded Joint

Simple Mechanism : Power Source at Bottom-Right Joint

Configure Power Source 2

Put the Power Source1s-red at the right Pin-Joint. The Mass2s 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 motor1s-red holds the mass in position.

Resolve Moments:

Resolve Moments gives the same Moment (Torque).

Tutorial and Reference Help Files for MechDesigner and MotionDesigner 13.2 + © Machine, Mechanism, Motion and Cam Design Software by PSMotion Ltd