2. 1
Table of Contents
1.0 EXISTING DESIGNS.........................................................................................................................2
1.1 Klann Linkage............................................................................................................................2
1.2 Jansen Linkage..........................................................................................................................2
1.3 Peaucellier-Lipkin Linkage..........................................................................................................3
2.0 THE DESIGN ..................................................................................................................................4
2.1 Legs..........................................................................................................................................6
2.2 Crank........................................................................................................................................6
2.3 Slider............................................................................................Error! Bookmark not defined.
2.4 Supports.......................................................................................Error! Bookmark not defined.
3.0 MATLAB SIMULATION ...................................................................................................................7
4.0 List of Tables and Figures...............................................................................................................9
5.0 References..................................................................................................................................10
3. 2
1.0 EXISTINGDESIGNS
1.1 Klann Linkage
The Klann Walker was discovered by Joe Klann, a Mechanical Engineer is a six bar linkage system that
simulates the walking mechanism of a legged animal. The walker consists of a frame,crank, two
couplers, and two grounded rockers. Specifically the two rocker arms are each individually considered as
one link, in addition to a connecting arm, a reciprocating leg and a finally a crank forming the last link.
The crank moves in a clockwise direction, and the following is the kinematic diagram of the Klann
Walker.
Figure 1 - Kinematic Diagram of the Klann (Unknown, Jansen - Klann Linkage Comparison, 2009)
The two rocker arms rotate so one is 180 degrees out of phase (lag) compared to the other, and in Figure 1
are labelled as the lower or upper rocker arm. Both rockers are connected to a stationary link (depicting
the ground) and to the crank via the coupler which connects both rocker arms to the crank. In addition a
connecting arm join the middle portion of both the upper and lower rocker arms in the same manner as
the link which joins the reciprocating (moving in opposite directions) legs. The green path shown in
Figure 1 is the path that the two rockers take upon initiation motion. (Klann, 2002)
1.2 Jansen Linkage
One of the most common types of walking mechanisms discovered was by Theo Jansen, a Kinetic
sculptor whose work shown to fuse the creative aspects of art together with the fundamental laws of
physics. He has been able to creatively design a 6 legged walking robot. Each leg has an 8 bar linkage
and 14 revolute joints, consisting of two ternary links attached to a four bar linkage and a crank. Three
legs are found on each side of the crank which is found to rotate counter-clockwise with a 120 degree lag
between each of the three legs on each side. Figure 2 is a skeletal illustration of this type of linkage
4. 3
Figure 2 - Kinematic Diagram of the Jansen Linkage (Kabai, 2010)
As seen in Figure 2, the four bar linkage connected to both rockers is shown to have a parallelogram
geometry. (Unknown, Jansen - Klann Linkage Comparison, 2009)
1.3 Peaucellier-Lipkin Linkage
The Peaucellier-Lipkin Linkage is one of the earliest type of planar mechanism that has the ability to form
straight line motion. Invented in 1864, the mechanism consists of an eight bar linkage and ten revolute
joints, and one degree of freedom. The kinematic illustration is shown below.
Figure 3 - KinematicDiagramof the Peaucellie-LipkinLinkage (Unknown,Peaucellier Exact Straight Line,
2010)
The Peaucellier-Lipkin linkage essentially converts circular input motion into straight line motion. Point
O4 in Figure 3 is fixed and point A is constrained (via revolute joints and fixed point) to move in a
circular path which goes through point O4 that ultimately forces point P (part of the 4 linkage square) to
trace out a linear path. The circular motion exhibited at point A is generated by a crankshaft. (Taimina,
2010)
3
5. 4
2.0 THE DESIGN
Objective
The crank-slider mechanism was utilized as the primary focus for the simulation of a fast “walking”
robot. The basic schematic is presented below:
Figure 4 – Concept schematic
Materials
1. Birch Wood
2. Plexiglas
3. Plastic tubing
4. Drinking Straws
5. Carpenter glue
6. Super glue
7. Glue sticks
8. Screws
9. Sand paper
10. Gear box
11. Batteries
12. Working tools (Sander, ruler, screw driver etc.)
6. 5
Method
Four major components comprising the Legs, Crank, Slider and Supports were each analyzed individually
and as a whole unit to optimize speed, and minimize friction. Using CATIA software a prototype of the
robot was generated and can be seen below.
Figure 5 - CATIA Full View
Figure 6 - CATIA Multi-view of ROBOT
7. 6
Figure 7 - Kinematic Diagram of ROBOT
2.1 Legs
The design of the legs was a critical factor in essentially determining the walking performance of the
robot. The legs had to be light-weight to reduce power consumption, and the shape had to be structured to
reduce any weight or foot forces produced from the ground acting on the robot. Four pairs of legs were
designed using light weight Birch. Each leg was constructed to be 25.5 cm in length from the crank joint
to ground to allow for a larger stride length between each walking cycle. For optimal performance the
shape of the legs were constructed to resemble those of an insect. Extensive studies centered on the
natural shape of an insect leg ultimately suggest that the center of gravity along the legs is always well
balanced, hence making it a good choice for shape. (Pringle, 1938) One set of legs was connected to the
crank via plastic tubes acting as the joints. Plastic was used primarily because of its low factor of friction,
and its cost.
2.2 Crank
The crank in a crank-slider mechanism is the rotating bar and it is connected via the leg to the slider. The
crank is powered by the motor via a set of batteries. This shaft is connected to the leg extremities, which
essentially allow the rotation of the 2 pairs of legs. Physically, the crank has to be able to provide
mechanical work to overcome the combined weight of the legs, in addition to any vibrations transmitted
by the motor. Also, a vital component in material selection was the weight of the crank. The crank had to
be light because the motor has a fairly low power output. Plexiglas was used as a material of choice for
the construction of the crank. Plexiglas is relatively light and shatter resistant; was measured to be
roughly 5mm in thickness. For two pair of legs, two cranks were placed opposite to each other, on each
side of the gear box. Both cranks were positioned 180 degrees out of phase for the purpose of simulating
the motion of two pair of legs moving off the ground on one side of the crank, while opposite to these two
legs (on the other end of the crank), another set of legs were moving towards the ground, in an alternating
or reciprocating fashion. All cranks, before installation, were carefully sanded using sand paper, along
there edges in an effort to minimize any friction effects between reciprocating legs.
8. 7
3.0 MATLAB SIMULATION
%Generate theta_2increments
clear
ratio=pi/180;
kappa=720;
theta_2=ratio*(1:kappa);
%Link length
r2=70;
r3=200;
if theta_2>0
omega_2=50;%angular speed of the crank
else omega_2=-50;
end
%Animation
figure
axis([-400 550 -400 400])
for i=1:kappa %Loop starts
kk=(r2/r3)*sin(theta_2(i));
phi_4(i)=asin(kk);
r1(i)=r2*cos(theta_2(i))+r3*cos(phi_4(i));
phidot_4(i)=(omega_2*(r2/r3)*cos(theta_2(i)))/sqrt(1-((r2/r3)*sin(theta_2(i)))^2);
char "Linear_Speed_of_the_Slider"
r1dot(i)=-r2*sin(theta_2(i))*omega_2-r3*sin(phi_4(i))*phidot_4(i)
char "Linear_Speed_of_the_Crank"
omega_2*r2
xl=r1(i)+115*cos(phi_4(i)+70)+r1dot(i)-115*phidot_4(i)*sin(phi_4(i)+70);
yl=(-115*sin(phi_4(i)+70))-115*phidot_4(i)*cos(phi_4(i)+70);
char "Linear_Speed_of_the_Leg_along_X-axis"
xl
char "Linear_Speed_of_the_Leg_along_X-axis"
yl
aa(1,:)=[0,0];
aa(2,:)=[r2*cos(theta_2(i)),r2*sin(theta_2(i))];
aa(3,:)=[r1(i),0];
aa(1,:)=[0,0]; %Closed chain
ll(4,:)=[r1(i),0];
ll(5,:)=[r1(i)+115*cos(phi_4(i)+70),-115*sin(phi_4(i)+70)];
ll(6,:)=[r2*cos(theta_2(i)),r2*sin(theta_2(i))];
ll(4,:)=[r1(i),0];
bb(7,:)=[r2*cos(theta_2(i)),r2*sin(theta_2(i))];
bb(8,:)=[r2*cos(theta_2(i))-
r2*omega_2*sin(theta_2(i))/100,r2*sin(theta_2(i))+r2*omega_2*cos(theta_2(i))/100];%To show the linear velocity
of the crank in the factor of 0.01
bb(7,:)=[r2*cos(theta_2(i)),r2*sin(theta_2(i))];
9. 8
cc(9,:)=[r1(i),0];
cc(10,:)=[r1(i)+r1dot(i)/100,0]; %To showthe linear velocity of the slider in the factor of 0.01
cc(9,:)=[r1(i),0];
dd(11,:)=[r2*cos(theta_2(i)),r2*sin(theta_2(i))];
dd(12,:)=[r1(i)+115*cos(phi_4(i)+70),-115*sin(phi_4(i)+70)];
dd(13,:)=[xl/10,yl/10];%To show the linear velocity of the leg in the factor of 0.1
dd(11,:)=[r2*cos(theta_2(i)),r2*sin(theta_2(i))];
plot(aa(:,1),aa(:,2),'o-',bb(:,1),bb(:,2),'-',cc(:,1),cc(:,2),'o-',ll(:,1),ll(:,2),'-',dd(:,1),dd(:,2),'-');
axis([-400 550 -400 400])
pause(0.01) % Set for animation speed
end%Loop ends
Figure 5 - MATLAB diagram of ROBOT's Leg
10. 9
4.0 List of Tables and Figures
Figure 1 - Kinematic Diagram of the Klann (Unknown, Jansen - Klann Linkage Comparison, 2009) ...........2
Figure 2 - Kinematic Diagram of the Jansen Linkage (Kabai, 2010)..........................................................3
Figure 3 - KinematicDiagramof the Peaucellie-LipkinLinkage (Unknown,PeaucellierExactStraightLine,
2010) .................................................................................................................................................3
Figure 4 - Concept Schematic..............................................................................................................5
Figure 5 - CATIA Full View....................................................................................................................5
Figure 6 - CATIA Multi-view of Robot...................................................................................................5
Figure 7 - Kinematic Diagram of ROBOT’s.............................................................................................6
Figure 8 - MATLAB diagram of ROBOT 's Leg.........................................................................................8
11. 10
5.0 References
Kabai,S. (2010). A Theo Jansen Walking Linkage.RetrievedApril4,2010, fromWolframMathematica:
http://demonstrations.wolfram.com/ATheoJansenWalkingLinkage/
Klann,J.C. (2002). United StatesPatent. RetrievedApril 4,2010, fromGoogle Patents:
http://www.google.com/patents?id=bQYKAAAAEBAJ&printsec=abstract&zoom=4#v=onepage&q&f=fals
e
Pringle,J.(1938). The Motor Mechanismof the InsectLeg. Departmentof Zoology ,220-231.
Taimina,D.(2010). How To Drawa StraightLine. RetrievedApril 4,2010, from KinematicModelsfor
Design:http://kmoddl.library.cornell.edu/tutorials/04/
Unknown.(2009). Jansen - Klann LinkageComparison.RetrievedApril 4,2010, fromMechanical Spider:
http://www.mechanicalspider.com/comparison.html
Unknown.(2010). Peaucellier Exact StraightLine. RetrievedApril 4,2010, from BrightHub:
http://www.brighthub.com/engineering/mechanical/articles/12903.aspx?image=2843
