This paper presents the analysis of a gravity compensated four-bar linkage mechanism with zero-free-length linear spring suspension. The objective of the study is to seek the possibility of employing the four-bar linkage or similar mechanisms for assisting vertical planar motion of a load mass in a gravitational field. The analysis is based on the system potential energy framework. Firstly, an arrangement of springs for gravity compensation in a four-bar linkage mechanism is proposed. It is then shown that for a four-bar linkage with symmetric geometric and mass properties the potential energy of the system has interesting and useful characteristics near the configuration at which the middle link is horizontal: an ideal operating configuration. The study also covers more practical cases where there is asymmetry in the mass distribution. The potential use of the mechanism in these cases is validated through a study of the sensitivity of the system potential energy function around the equilibrium point. Finally, based on the results obtained a novel mechanism is proposed for achieving gravity compensated vertical plane motion of a load mass. The proposed mechanism can have a wide range of travel and has significant potential for use not only in low-speed mechanical systems but also in high-speed heavy automated systems, where operating accelerations are of the order of $1g$ or less.

1.
Nathan
,
R. H.
, 1985, “
A Constant Force Generation Mechanism
,”
ASME J. Mech., Transm., Autom. Des.
0738-0666,
107
, pp.
508
512
.
2.
Wongratanaphisan
,
T.
, and
Chew
,
M.
, 2002, “
Gravity Compensation of Spatial Two-dof Serial Manipulators
,”
J. Rob. Syst.
0741-2223,
19
(
7
), pp.
329
347
.
3.
Wongratanaphisan
,
T.
, and
Chew
,
M.
, 2001, “
Gravity Compensation of Industrial Robots
,”
The Second Asian Symposium on Industrial Automation and Robotics
,
Bangkok, Thailand
, May.
4.
Streit
,
D. A.
, and
Shin
,
E.
, 1993, “
,”
ASME J. Mech. Des.
1050-0472,
115
, pp.
604
611
.
5.
,
S.
,
Streit
,
D. A.
, and
Gilmore
,
B. J.
, 1993, “
Elastic Potential Synthesis—A Generalized Procedure for Dynamic Synthesis of Machine and Mechanism Systems
,”
ASME J. Mech. Des.
1050-0472,
115
, pp.
568
575
.
6.
Shin
,
E.
, and
Streit
,
D. A.
, 1991, “
Spring Equilibrator Theory for Static Balancing of Planar Pantograph Linkages
,”
Mech. Mach. Theory
0094-114X,
26
(
7
), pp.
645
657
.
7.
Shin
,
E.
, and
Streit
,
D. A.
, 1993, “
An Energy Efficient Quadruped With Two-Stage Equilibrator
,”
ASME J. Mech. Des.
1050-0472,
115
, pp.
156
163
.
8.
Agrawal
,
S. K.
,
Gardner
,
G.
, and
Pledgie
,
S.
, 2001, “
Design and Fabrication of an Active Gravity Balanced Planar Mechanism Using Auxiliary Parallelograms
,”
ASME J. Mech. Des.
1050-0472,
123
(
4
), pp.
525
528
.
9.
Laliberte
,
T.
,
Gosselin
,
C. M.
, and
Jean
,
M.
, 1999, “
Static Balancing of 3-dof Planar Parallel Mechanisms
,”
IEEE/ASME Trans. Mechatron.
1083-4435,
4
(
4
), pp.
363
377
.
10.
Streit
,
D. A.
,
Chuang
,
H.
, and
Gilmore
,
B. J.
, 1991, “
Perfect Equilibrators for Rigid Body Spatial Rotations About a Hooke’s Joint
,”
ASME J. Mech. Des.
1050-0472,
113
, pp.
500
507
.
11.
Walsh
,
G. J.
,
Streit
,
D. A.
, and
Gilmore
,
B. J.
, 1991, “
Spatial Spring Equilibrator Theory
,”
Mech. Mach. Theory
0094-114X,
26
(
2
), pp.
155
170
.
12.
Gosselin
,
C. M.
, 1999, “
Static Balancing of Spherical 3-dof Parallel Mechanisms and Manipulator
,”
Int. J. Robot. Res.
0278-3649,
18
(
7
), pp.
819
829
.
13.
Wang
,
J.
, and
Gosselin
,
C. M.
, 2000, “
Static Balancing of Spatial Four-Degree-of-Freedom Parallel Mechanisms
,”
Mech. Mach. Theory
0094-114X,
35
(
4
), pp.
563
592
.
14.
Wang
,
J.
, and
Gosselin
,
C. M.
, 1999, “
Static Balancing of Spatial Three-Degree-of-Freedom Parallel Mechanisms
,”
Mech. Mach. Theory
0094-114X,
34
(
3
), pp.
437
452
.
15.
Gosselin
,
C. M.
, and
Wang
,
J.
, 2000, “
Static Balancing of Spatial Six-Degree-of-Freedom Parallel Mechanisms With Revolute Actuators
,”
J. Rob. Syst.
0741-2223,
17
(
3
), pp.
159
170
.
16.
Fattah
,
A.
, and
Agrawal
,
S. K.
, 2005, “
On the Design of a Passive Orthosis to Gravity Balance Human Legs
,”
ASME J. Mech. Des.
1050-0472,
127
(
4
), pp.
802
808
.
17.
Fattah
,
A.
,
Agrawal
,
S. K.
,
Catlin
,
G.
, and
Hamnett
,
J.
, 2006, “
Design of a Passive Gravity-Balanced Assistive Device for Sit-to-Stand Tasks
,”
ASME J. Mech. Des.
1050-0472,
128
, pp.
1122
1129
.