﻿ Six-bar Kinematic-chains: Watt and Stephenson

# Tutorial 2A: Six-bar Kinematic-Chains

## Six-bar Kinematic-Chains

### Objectives of this Tutorial

To learn how to add dyads to kinematic-chains. You will see that you can, in principle, add any number of dyads to each kinematic-chain.

In this tutorial, we will:

 1 Add RRR and RRP dyads to build slightly more complex kinematic-chains.
 2 Show that a:
 a. Slide-Joint does not need to use the CAD-Line along the Part's centre.
 b. Pin-Joint does not necessarily need to use the start-Point or end-Point of the CAD-Line along the Part's centre.
 3 Learn a little about six-bar* kinematic-chains.

* The term 'bar' is used more frequently than 'Part' when applied to mechanisms such as: four-bar, six-bar, eight-bar.

 ➢ 6-bar Kinematic-Chains: Crank + RRR + RRR - only Pin-Joints.
 ➢ 6-Bar Kinematic-Chains: Crank + RRR + RRP - Pin-Joints and one Slide-Joint.

Then, experiment with different possibilities of the three joints in a Dyad: RRR, RRP, RPR, RPP, PRP

Also, change the driven Part from a Rocker to a Slider.

#### Degrees-of-Freedom of Dyads and Motion-Parts

A new dyad does not change the number of degrees-of-freedom (DOF) in a kinematic-chain.

Why? Because a dyad has two Parts and three Joints.

 • Each Part adds 3 DOF*. Thus, two new Parts add to the model:  +2Parts × +3DOF = +6DOF
 • Each Joint removes 2 DOF£. Thus, three new Joints remove from the model: +3Joints × – 2DOF = – 6DOF

Thus, the change to the total Degrees-of-Freedom = +6 + (– 6) = 0(Zero).

* Parts on a Plane.

£ Pin-Joint or Slide-Joints added to Parts on a Plane.

Motion-Parts see the Kinematics-Tree

A Motion-Part does not change the degrees-of-freedom of a kinematic-chain.

Why?  Because a Motion-Part has one Part, one Joint and one Motion-Dimension (a defined coordinate).

 • Each Part adds 3 DOF. Thus one new Part in a Motion-Part: 1Part × +3DOF = +3DOF
 • Each Joint removes 2 DOF. Thus, one new Joint removes from the model: +1Joint × –2DOF = –2DOF
 • Each Motion-Dimension removes 1 DOF. Thus, one new Motion Dimension: +1MD × –1DOF = –1 DOF

Thus, the change to the total Degrees-of-Freedom = +3 +(–2) + (–1) = 0(Zero).

Kinematically-defined Parts & Green Parts