# Estimation of the Abduction/Adduction Movement of the Metacarpophalangeal Joint of the Thumb
## 1 Introduction  
The thumb is essential for grasping, as it leads the motion of the other digits [1]. The opposition of the thumb to the fingers is essential for grasping [2] and is part of most grasp positions needed to carry out activities of daily living (ADL) [3]. From the mechanical point of view, this complex movement is performed mainly at the thumb metacarpophalangeal (MCP) and carpometacarpal (CMC) joints and involves several motions: thumb CMC flexion and abduction, and thumb MCP flexion and abduction.  
The thumb MCP joint is of the condylar type, whereas the thumb CMC joint is a saddle joint, both of them having two main degrees of freedom (DoF): flexion--extension and abduction/adduction, defined as rotations around two non-perpendicular and non-intersecting axes on each joint [4]. At the MCP joint, the flexion-extension axis is in the metacarpal passing under the epicondyles, and the abduction/adduction axis is in the proximal phalanx, passing between the sesamoids just proximal to its beak. At the CMC joint, the flexion/extension axis is in the trapezium and the abduction/adduction axis is in the metacarpal, their positions being constant throughout the range of motion of the joint, and not perpendicular to the bones [5]. As the axes are non-perpendicular and non-intersecting, it is difficult to assign classic planes to thumb movements and postures, leading to different ways of defining the thumb motion [6]. For this reason, some studies also consider pronation at the CMC joint, although the most widely accepted kinematic model is to use only five DoF: CMC flexion-extension and abduction/adduction, MCP flexion-extension and abduction/adduction, and interphalangeal (IP) flexion-extension.  
Interestingly, all the muscles that are abductors or adductors of the MCP joint are also abductors or adductors of the CMC joint. This sophisticated biomechanical structureunderlies a dimensionality reduction mechanism during motion control due to the existence of intra-thumb muscular synergies [7]. This actuation linkage, together with the tendons configuration of the MCP joint, results in a very limited capacity for independent abduction of the MCP joint, which means that movements of the thumb MCP joint are closely linked to the movements of the thumb CMC joint [4; 8]. In this regard, [PERSON] and [PERSON] [8] analyzed the global coordination of the thumb during free movements (opposition and circumduction), which revealed coordination between the flexion and pronation at the CMC joint, and between the flexion of the CMC joint and the MCP joint. However, no previous work has studied the correlation between thumb joints during the common grasps used to perform ADL.  
In addition, the high number of thumb DoF in a fairly small space makes it a challenging task to record in vivo joint rotations accurately. As a consequence, many devices used to measure the kinematics of the hand (such as instrumented gloves, e.g., Cyberglove) do not implement sensors to measure the MCP abduction movement [9], and many kinematic studies in the literature do not consider this movement, although in some cases they do use devices capable of measuring it [10; 11]. This approximation may lead to important implications for the accuracy of biomechanical models [12; 13].  
This work has two aims: (1) to examine the correlation between thumb joints during grasps, and (2) to obtain the equation that allows the thumb MCP abduction/adduction movement to be estimated from the other joint motions of the thumb during the commonest grasps used during ADL.