INTRODUCTION

This Data Item presents the analytical methods used to estimate
numerical values of reaction forces at joints that connect links of
single degree-of-freedom, planar, multibar linkage mechanisms.
Force analysis is an essential feature of the design of linkages
used in industrial machinery because it can lead to improved
reliability combined with higher operating speeds and loads.

It is advisable, during the design of a new mechanism, to obtain
estimates of the joint forces^† once the link lengths
have been determined. Provisional values of cross-sectional
geometry and a suitable material should be chosen for each moving
link. Force analysis gives provisional values of joint forces which
are then used to estimate the stresses in individual links and the
deflections of important points on those links. The proposed
cross-sectional geometry and material may then be altered and the
joint forces re-determined in an iterative process until an
acceptable design is obtained. Also estimates of joint forces are
used to determine appropriate bearing types and sizes. Values of
frame shaking force and frame shaking moment are essential when
designing the fixed machine frame and when deciding whether it is
necessary to balance a linkage. Force values are used to compare
the performance of alternative linkage configurations and to
evaluate the effect of introducing different balancing techniques
(see References 9, 10 and 11).

Traditionally, values of the necessary kinematic and dynamic
quantities are obtained by a laborious graphical approach. Modern
methods are based on the derivation of numerous equations
describing the kinematic relationships and the equilibrium
conditions followed by numerical solution of these equations using
a computer. Three general strategies for estimating joint forces
are described in this Item.

(a) Static force analysis

Inertia is ignored and the reactions at the joints due only to
the external force are determined. Each joint force is expressed as
a function of the position of the input link and the linkage is
assumed to be stationary at each position. Static force analysis is
suitable only for the analysis of very slow moving linkages.

(b) Kinetostatic force analysis

The reactions at the joints due to inertia and external forces
are determined. Each joint force is expressed as a function of the
position of the input link and the motion of the input link is
assumed to be known. A commonly-used assumption is that the
mechanism is driven via an input crank rotating at constant angular
velocity.

The reactions at the joints due to inertia and external forces
are determined. Each joint force is expressed as a function of time
and the driving force or torque is assumed to be known as a
function of time, input link position or input link velocity.

The development of rigid-body mathematical models of linkages
using these strategies is demonstrated in this Item. The range of
application and the advantages and limitations of each method are
stated. The wide variety of linkage configurations used in
industrial machinery and the different loading conditions of each
machine make the presentation of generic design data impractical.
Consequently the aim of this Data Item is to provide a simple
framework for the development of computer-based methods for
analysis of linkages in particular applications. Section 11
contains the equations required to determine the joint forces by
kinetostatic force analysis for commonly-used four-bar linkages. A
computer program implementing kinetostatic force analysis of
four-bar planar linkages is included in Section 12.

^† See Section 2.2 for definitions