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, ...
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
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).
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.