﻿ Six-bar Kinematic-chains: Watt and Stephenson

# Tutorial 2A: Six-bar Kinematic-Chains

## Six-bar Kinematic-Chains

#### Objectives of this Tutorial

To learn that a Dyad does not change the degrees-of-freedom [DOF] of a kinematic-chain.

When all Parts are kinematically-defined and have Green Part-Outlines before you add a Dyad, all Parts will be kinematically-defined and have Green Part-Outlines after you add a Dyad.

All Dyads have two Parts and three Joints.

In this tutorial, we will:

 1 Add R-R-R and R-R-P dyads to build slightly more complex kinematic-chains.
 o 'R' Joints are Revolute Joints, which are identical to Pin-Joints.
 o 'P' Joints are Prismatic Joints, which are identical to Slide-Joints.
 2 Demonstrate that a:
 b. Pin-Joint is not always at the start-Point or end-Point of the CAD-Line of Added-Parts.
 3 Learn a little about six-bar* kinematic-chains.

* The term bar is used more frequently than Part when we apply the term to mechanisms. For example four-bar, six-bar, eight-bar...

#### Terminology: Degrees-of-Freedom[DOF] : Dyads & Motion-Parts

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

Why? Each dyad has two Parts and three Joints:

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

Thus, the total DOF = +6 + (– 6) = 0.

*Parts on the Mechanism-Plane

Motion-Parts :

See the Rockers or Slider in the Kinematics-Tree

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

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

 • Each Part adds 3 DOF. One 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).