Tutorial 2B: Six-bar Kinematic-Chains

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Tutorial 2B: Six-bar Kinematic-Chains

Six-bar Kinematic-Chains

Objectives of this Tutorial

To learn more about dyads (Also called Assur Groups)

To learn how to add dyads to a kinematically-defined chain.

To learn that a dyad does not change the degrees-of-freedom (DOF) of a kinematic-chain.

IMPORTANT concepts about DYADS

All Dyads have two Parts and three Joints.

If a kinematic-chain is a kinematically-defined chain before you add a new dyad, it will also be a kinematically-defined chain after you add a dyad.

In this tutorial, we will:

1.Add R-R-R and R-R-P dyads to build slightly more complex kinematic-chains.

oR Joints are Revolute-Joints. They are identical to Pin-Joints.

oP Joints are Prismatic-Joints. They are identical to Slide-Joints.

2.Demonstrate that a:

a.Slide-Joint is not always between the CAD-Lines along the X-axes of Parts.

b.Pin-Joint is not always at the start-Point or end-Point of the CAD-Line of 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, ...

Degrees-of-Freedom(DOF) : Dyads & Motion-Parts

Dyads :

See also Kinematics-Tree.

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 adds 3 DOF*. Two Parts:  2 × +3×DOF = +6×DOF

Each Joint removes 2 DOF. Three Joints: 3 × –2×DOF = –6×DOF

Thus, the total DOF = +6 + (– 6) = 0.

*Parts on the Mechanism-Plane

Motion-Parts :

See the Rockers and Slider in the Kinematics-Tree

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

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

Each Part adds 3 DOF. One Part: 1×Part × +3×DOF = +3×DOF

Each Joint removes 2 DOF. One Joint: +1×Joint × –2×DOF = –2×DOF

A Motion-Dimension removes 1 DOF : +1×MD × –1×DOF = –1×DOF

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

Step by Step Instructions

Add more Dyads

6-bar Kinematic-Chains: Crank + R-R-R + R-R-R - only Pin-Joints.

6-Bar Kinematic-Chains: Crank + R-R-R + R-R-P - Pin-Joints and one Slide-Joint.

Experiment with different possibilities of the three joints in a Dyad: R-R-R, R-R-P, RPR, RPP, PRP

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